메뉴 건너뛰기




Volumn 36, Issue 3, 1999, Pages 271-296

Strong shift equivalence theory and the shift equivalence problem

Author keywords

Positivity; Strong shift equivalence; The shift equivalence problem

Indexed keywords


EID: 0033446503     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0273-0979-99-00798-3     Document Type: Article
Times cited : (30)

References (144)
  • 2
    • 0022029759 scopus 로고    scopus 로고
    • R.L. Adler, The torus and the disk, IBM Journal of Research and Development, Vol. 31, No.2, March 1987, 224-234 CMP 19:14
    • CMP , vol.19 , pp. 14
  • 3
    • 84968500701 scopus 로고    scopus 로고
    • Topological entropy
    • R.L. Adler, A. Konheim, and M. McAndrew, Topological entropy, TAMS 114, 1965, 309-319 MR 30:5291
    • (1965) TAMS , vol.114 , pp. 309-319
    • Adler, R.L.1    Konheim, A.2    McAndrew, M.3
  • 4
    • 84968500701 scopus 로고    scopus 로고
    • R.L. Adler, A. Konheim, and M. McAndrew, Topological entropy, TAMS 114, 1965, 309-319 MR 30:5291
    • MR , vol.30 , pp. 5291
  • 5
    • 0001588027 scopus 로고    scopus 로고
    • Strong shift equivalence of 2 × 2 matrices of non-negative integers
    • K. Baker, Strong shift equivalence of 2 × 2 matrices of non-negative integers, ETDS, 1983, 3, 501-508 MR 86g:28021
    • (1983) ETDS , vol.3 , pp. 501-508
    • Baker, K.1
  • 6
    • 0001588027 scopus 로고    scopus 로고
    • K. Baker, Strong shift equivalence of 2 × 2 matrices of non-negative integers, ETDS, 1983, 3, 501-508 MR 86g:28021
    • MR , vol.86 G , pp. 28021
  • 7
    • 51649159715 scopus 로고    scopus 로고
    • Algebraic K-theory and crystalline cohomology
    • S. Bloch, Algebraic K-theory and crystalline cohomology, Pub. Math. IHES 47, 1977, 197-238 MR81j:14011
    • (1977) Pub. Math. IHES , vol.47 , pp. 197-238
    • Bloch, S.1
  • 8
    • 51649159715 scopus 로고    scopus 로고
    • S. Bloch, Algebraic K-theory and crystalline cohomology, Pub. Math. IHES 47, 1977, 197-238 MR81j:14011
    • MR , vol.81 J , pp. 14011
  • 9
    • 0002077980 scopus 로고
    • The stochastic shift equivalence conjecture is false
    • M. Boyle, The stochastic shift equivalence conjecture is false, Contemporary Mathematics, Vol. 135, 1992, 107-110 MR 93i:28013
    • (1992) Contemporary Mathematics , vol.135 , pp. 107-110
    • Boyle, M.1
  • 10
    • 0040562454 scopus 로고    scopus 로고
    • M. Boyle, The stochastic shift equivalence conjecture is false, Contemporary Mathematics, Vol. 135, 1992, 107-110 MR 93i:28013
    • MR , vol.93 I , pp. 28013
  • 11
    • 0001300739 scopus 로고
    • Markov partitions for axiom a diffeomorphisms
    • R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. Jour. Math. 92, 1970, 725-747 MR 43:2740
    • (1970) Amer. Jour. Math. , vol.92 , pp. 725-747
    • Bowen, R.1
  • 12
    • 0039969601 scopus 로고    scopus 로고
    • R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. Jour. Math. 92, 1970, 725-747 MR 43:2740
    • MR , vol.43 , pp. 2740
  • 13
    • 84971916787 scopus 로고    scopus 로고
    • The action of inert finite order automorphisms on finite subsystems
    • M. Boyle and U.Fiebig, The action of inert finite order automorphisms on finite subsystems, ETDS 11, 1991, 413-425 MR 92g:58029
    • (1991) ETDS , vol.11 , pp. 413-425
    • Boyle, M.1    Fiebig, U.2
  • 14
    • 84971916787 scopus 로고    scopus 로고
    • M. Boyle and U.Fiebig, The action of inert finite order automorphisms on finite subsystems, ETDS 11, 1991, 413-425 MR 92g:58029
    • MR , vol.92 G , pp. 58029
  • 15
    • 84968493697 scopus 로고    scopus 로고
    • Algebraic shift equivalence and primitive matrices
    • M. Boyle and D. Handelman, Algebraic shift equivalence and primitive matrices, Trans. AMS 336, No. 1, 1993, 121-149. MR 93e:58050
    • (1993) Trans. AMS , vol.336 , Issue.1 , pp. 121-149
    • Boyle, M.1    Handelman, D.2
  • 16
    • 84968493697 scopus 로고    scopus 로고
    • M. Boyle and D. Handelman, Algebraic shift equivalence and primitive matrices, Trans. AMS 336, No. 1, 1993, 121-149. MR 93e:58050
    • MR , vol.93 E , pp. 58050
  • 17
    • 0001100975 scopus 로고
    • The spectra of nonnegative matrices via symbolic dynamics
    • _, The spectra of nonnegative matrices via symbolic dynamics, Annals of Mathematics, 133, 1991, 249-316 MR 92d:58057
    • (1991) Annals of Mathematics , vol.133 , pp. 249-316
  • 18
    • 0041156546 scopus 로고    scopus 로고
    • _, The spectra of nonnegative matrices via symbolic dynamics, Annals of Mathematics, 133, 1991, 249-316 MR 92d:58057
    • MR , vol.92 D , pp. 58057
  • 19
    • 0002355541 scopus 로고    scopus 로고
    • Periodic points and automorphisms of the shift
    • M. Boyle and W. Krieger, Periodic points and automorphisms of the shift, Trans. AMS 302, 1987, 125-149 MR 88g:54065
    • (1987) Trans. AMS , vol.302 , pp. 125-149
    • Boyle, M.1    Krieger, W.2
  • 20
    • 0002355541 scopus 로고    scopus 로고
    • M. Boyle and W. Krieger, Periodic points and automorphisms of the shift, Trans. AMS 302, 1987, 125-149 MR 88g:54065
    • MR , vol.88 G , pp. 54065
  • 21
    • 0002193133 scopus 로고    scopus 로고
    • Automorphisms and subsystems of the shift
    • _, Automorphisms and subsystems of the shift, Jour. Reine Angew. Math. 437, 1993, 13-28 MR 95b:54051
    • (1993) Jour. Reine Angew. Math. , vol.437 , pp. 13-28
  • 22
    • 0002193133 scopus 로고    scopus 로고
    • _, Automorphisms and subsystems of the shift, Jour. Reine Angew. Math. 437, 1993, 13-28 MR 95b:54051
    • MR , vol.95 B , pp. 54051
  • 23
    • 84956252003 scopus 로고    scopus 로고
    • The automorphism group of a shift of finite type
    • M. Boyle, D. Lind, and D. Rudolph, The automorphism group of a shift of finite type, Trans. AMS 306, 1988, 71-114 MR 89m:54051
    • (1988) Trans. AMS , vol.306 , pp. 71-114
    • Boyle, M.1    Lind, D.2    Rudolph, D.3
  • 24
    • 84956252003 scopus 로고    scopus 로고
    • M. Boyle, D. Lind, and D. Rudolph, The automorphism group of a shift of finite type, Trans. AMS 306, 1988, 71-114 MR 89m:54051
    • MR , vol.89 M , pp. 54051
  • 25
    • 0003309731 scopus 로고
    • Resolving maps and the dimension group for shifts of finite type
    • Number 377, Providence, R.I.
    • M. Boyle, B. Marcus, and P. Trow, Resolving maps and the dimension group for shifts of finite type, Mem. Amer. Math. Soc. vol. 70 (1987), Number 377, Providence, R.I. MR 89c:28019
    • (1987) Mem. Amer. Math. Soc. , vol.70
    • Boyle, M.1    Marcus, B.2    Trow, P.3
  • 26
    • 0039377247 scopus 로고    scopus 로고
    • M. Boyle, B. Marcus, and P. Trow, Resolving maps and the dimension group for shifts of finite type, Mem. Amer. Math. Soc. vol. 70 (1987), Number 377, Providence, R.I. MR 89c:28019
    • MR , vol.89 C , pp. 28019
  • 28
    • 0040562441 scopus 로고    scopus 로고
    • Simple connectivity of the Markov partition space
    • preprint, UC Berkeley
    • L. Badoian and J.B. Wagoner, Simple connectivity of the Markov partition space, preprint, UC Berkeley, 1998, to appear in Pac. Jour. Math.
    • (1998) Pac. Jour. Math.
    • Badoian, L.1    Wagoner, J.B.2
  • 29
    • 51249187294 scopus 로고    scopus 로고
    • La stratification naturelle des espaces de fonctions différentiables ré elles et le theoreme de la pseudo-isotopie
    • J. Cerf, La stratification naturelle des espaces de fonctions différentiables ré elles et le theoreme de la pseudo-isotopie, Publ. Math. IHES, No. 39, 1970, 5-173 MR 45:1176
    • (1970) Publ. Math. IHES , vol.39 , pp. 5-173
    • Cerf, J.1
  • 30
    • 51249187294 scopus 로고    scopus 로고
    • J. Cerf, La stratification naturelle des espaces de fonctions différentiables ré elles et le theoreme de la pseudo-isotopie, Publ. Math. IHES, No. 39, 1970, 5-173 MR 45:1176
    • MR , vol.45 , pp. 1176
  • 31
    • 0001899289 scopus 로고    scopus 로고
    • Topological Markov chains and dicyclic dimension groups
    • J. Cuntz and W. Krieger, Topological Markov chains and dicyclic dimension groups, J. Reine Angew. Math. 320, 1980, 44-51 MR 81m:54074
    • (1980) J. Reine Angew. Math. , vol.320 , pp. 44-51
    • Cuntz, J.1    Krieger, W.2
  • 32
    • 0001899289 scopus 로고    scopus 로고
    • J. Cuntz and W. Krieger, Topological Markov chains and dicyclic dimension groups, J. Reine Angew. Math. 320, 1980, 44-51 MR 81m:54074
    • MR , vol.81 M , pp. 54074
  • 33
    • 0001175308 scopus 로고    scopus 로고
    • A class of C*-algebras and topological Markov chains
    • _, A class of C*-Algebras and topological Markov chains, Inventiones Math. 56, 1980, 251-268 MR 82f:46073a
    • (1980) Inventiones Math. , vol.56 , pp. 251-268
  • 34
    • 0001175308 scopus 로고    scopus 로고
    • _, A class of C*-Algebras and topological Markov chains, Inventiones Math. 56, 1980, 251-268 MR 82f:46073a
    • MR , vol.82 F
  • 35
    • 0003336982 scopus 로고
    • Dimensions and C* algebras
    • AMS
    • E.G. Effros, Dimensions and C* Algebras, CBMS No. 46, AMS, 1981 MR 84k:46042
    • (1981) CBMS , vol.46
    • Effros, E.G.1
  • 36
    • 0041156543 scopus 로고    scopus 로고
    • E.G. Effros, Dimensions and C* Algebras, CBMS No. 46, AMS, 1981 MR 84k:46042
    • MR , vol.84 K , pp. 46042
  • 37
    • 0002248535 scopus 로고    scopus 로고
    • Gyration numbers for involutions of subshifts of finite type I
    • U. Fiebig, Gyration numbers for involutions of subshifts of finite type I, Forum Math. 4, 1992, 77-108; and II, Forum Math.4, 1992, 183-211 MR 93g:58041; MR 93g:58042
    • (1992) Forum Math. , vol.4 , pp. 77-108
    • Fiebig, U.1
  • 38
    • 0002248535 scopus 로고    scopus 로고
    • U. Fiebig, Gyration numbers for involutions of subshifts of finite type I, Forum Math. 4, 1992, 77-108; and II, Forum Math.4, 1992, 183-211 MR 93g:58041; MR 93g:58042
    • (1992) II, Forum Math. , vol.4 , pp. 183-211
  • 39
    • 0002248535 scopus 로고    scopus 로고
    • U. Fiebig, Gyration numbers for involutions of subshifts of finite type I, Forum Math. 4, 1992, 77-108; and II, Forum Math.4, 1992, 183-211 MR 93g:58041; MR 93g:58042
    • MR , vol.93 G , pp. 58041
  • 40
    • 0002248535 scopus 로고    scopus 로고
    • U. Fiebig, Gyration numbers for involutions of subshifts of finite type I, Forum Math. 4, 1992, 77-108; and II, Forum Math.4, 1992, 183-211 MR 93g:58041; MR 93g:58042
    • MR , vol.93 G , pp. 58042
  • 41
    • 0001776020 scopus 로고
    • Homology and dynamical systems
    • AMS
    • J. Franks, Homology and dynamical systems, CBMS No. 49, AMS, 1982 MR 84f:58067
    • (1982) CBMS , vol.49
    • Franks, J.1
  • 42
    • 0039969593 scopus 로고    scopus 로고
    • J. Franks, Homology and dynamical systems, CBMS No. 49, AMS, 1982 MR 84f:58067
    • MR , vol.84 F , pp. 58067
  • 43
    • 0039626196 scopus 로고    scopus 로고
    • Invariants for one-dimensional cohomology classes arising from TQFT
    • P.M. Gilmer, Invariants for one-dimensional cohomology classes arising from TQFT, Topology and its Applications 75, 1997, 217-259 MR 97k:57018
    • (1997) Topology and Its Applications , vol.75 , pp. 217-259
    • Gilmer, P.M.1
  • 44
    • 0039626196 scopus 로고    scopus 로고
    • P.M. Gilmer, Invariants for one-dimensional cohomology classes arising from TQFT, Topology and its Applications 75, 1997, 217-259 MR 97k:57018
    • MR , vol.97 K , pp. 57018
  • 45
    • 0040562445 scopus 로고    scopus 로고
    • Topological quantum field theory and strong shift equivalence
    • preprint from Louisiana State University
    • _, Topological quantum field theory and strong shift equivalence, preprint from Louisiana State University, 1997, to appear in Bulletin of the Canadian Mathematical Society
    • (1997) Bulletin of the Canadian Mathematical Society
  • 46
    • 0039377242 scopus 로고
    • 2 of some truncated polynomial rings
    • Ring Theory Waterloo, Springer-Verlag
    • 2 of some truncated polynomial rings, Ring Theory Waterloo, Springer-Verlag LNM 734, 1979, 249-278 MR 80k:13005
    • (1979) LNM , vol.734 , pp. 249-278
    • Geller, S.1    Roberts, L.2
  • 47
    • 85087242633 scopus 로고    scopus 로고
    • 2 of some truncated polynomial rings, Ring Theory Waterloo, Springer-Verlag LNM 734, 1979, 249-278 MR 80k:13005
    • MR , vol.80 K , pp. 13005
  • 48
    • 0001072208 scopus 로고    scopus 로고
    • Endomorphisms and automorphisms of shift dynamical systems
    • G. Hedlund, Endomorphisms and automorphisms of shift dynamical systems, Math. Systems Theory 3, 1969, 320-375 MR 41:4510
    • (1969) Math. Systems Theory , vol.3 , pp. 320-375
    • Hedlund, G.1
  • 49
    • 0001072208 scopus 로고    scopus 로고
    • G. Hedlund, Endomorphisms and automorphisms of shift dynamical systems, Math. Systems Theory 3, 1969, 320-375 MR 41:4510
    • MR , vol.41 , pp. 4510
  • 50
    • 0003234294 scopus 로고
    • Pseudo isotopies of compact manifolds
    • Société Mathématique de France
    • A. Hatcher and J.B. Wagoner, Pseudo Isotopies of Compact Manifolds, Astérisque No. 6, Société Mathématique de France, 1973 MR 50:5821
    • (1973) Astérisque , vol.6
    • Hatcher, A.1    Wagoner, J.B.2
  • 51
    • 0040562446 scopus 로고    scopus 로고
    • A. Hatcher and J.B. Wagoner, Pseudo Isotopies of Compact Manifolds, Astérisque No. 6, Société Mathématique de France, 1973 MR 50:5821
    • MR , vol.50 , pp. 5821
  • 53
    • 0039969595 scopus 로고    scopus 로고
    • B. Kitchens, Symbolic dynamics, one-sided, two-sided and countable state Markov shifts, Springer-Verlag, 1998 MR 98k:58079
    • MR , vol.98 K , pp. 58079
  • 55
    • 0002200050 scopus 로고    scopus 로고
    • 2, Journal of Algebra, 1978, 159-177 MR 80a:18013
    • MR , vol.80 A , pp. 18013
  • 56
    • 0001450585 scopus 로고
    • New metric invariants of transitive dynamical systems and automorphisms of Lebesgue spaces
    • A.N. Kolomogorov, New metric invariants of transitive dynamical systems and automorphisms of Lebesgue spaces, Dokl. Akad. Nauk. SSSR, 119, 1958, 861-864
    • (1958) Dokl. Akad. Nauk. SSSR , vol.119 , pp. 861-864
    • Kolomogorov, A.N.1
  • 57
    • 0001175312 scopus 로고    scopus 로고
    • On dimension functions and topological Markov chains
    • W. Krieger, On dimension functions and topological Markov chains, Invent. Math. 56, 1980, 239-250 MR 81m:28018
    • (1980) Invent. Math. , vol.56 , pp. 239-250
    • Krieger, W.1
  • 58
    • 0001175312 scopus 로고    scopus 로고
    • W. Krieger, On dimension functions and topological Markov chains, Invent. Math. 56, 1980, 239-250 MR 81m:28018
    • MR , vol.81 M , pp. 28018
  • 60
    • 0000052551 scopus 로고
    • Some results on decidability of shift equivalence
    • K.H. Kim and F.W. Roush, Some results on decidability of shift equivalence, J. Comb. Inform. System Sci. 4, 1979, 123-146. MR 81m:58064
    • (1979) J. Comb. Inform. System Sci. , vol.4 , pp. 123-146
    • Kim, K.H.1    Roush, F.W.2
  • 61
    • 0041156541 scopus 로고    scopus 로고
    • K.H. Kim and F.W. Roush, Some results on decidability of shift equivalence, J. Comb. Inform. System Sci. 4, 1979, 123-146. MR 81m:58064
    • MR , vol.81 M , pp. 58064
  • 62
    • 0002079530 scopus 로고
    • Decidability of shift equivalence
    • J. W. Alexander, ed., Springer-Verlag, Heidelberg
    • _, Decidability of shift equivalence, in J. W. Alexander, ed., Dynamical Systems, Lecture Notes in Mathematics, vol. 1342, Springer-Verlag, Heidelberg, 1988 MR 90g:54033
    • (1988) Dynamical Systems, Lecture Notes in Mathematics , vol.1342
  • 63
    • 0041156538 scopus 로고    scopus 로고
    • _, Decidability of shift equivalence, in J. W. Alexander, ed., Dynamical Systems, Lecture Notes in Mathematics, vol. 1342, Springer-Verlag, Heidelberg, 1988 MR 90g:54033
    • MR , vol.90 G , pp. 54033
  • 64
    • 0003120829 scopus 로고
    • On the structure of inert automorphisms of subshifts
    • _, On the structure of inert automorphisms of subshifts, Pure Mathematics and Applications 2, 1991, 3-22 MR 94c:58056
    • (1991) Pure Mathematics and Applications , vol.2 , pp. 3-22
  • 65
    • 0041156540 scopus 로고    scopus 로고
    • _, On the structure of inert automorphisms of subshifts, Pure Mathematics and Applications 2, 1991, 3-22 MR 94c:58056
    • MR , vol.94 C , pp. 58056
  • 66
    • 84968502752 scopus 로고    scopus 로고
    • Williams's conjecture is false for reducible subshifts
    • _, Williams's conjecture is false for reducible subshifts, Jour. AMS 5, 1992, 213-215 MR 92j:54055
    • (1992) Jour. AMS , vol.5 , pp. 213-215
  • 67
    • 84968502752 scopus 로고    scopus 로고
    • _, Williams's conjecture is false for reducible subshifts, Jour. AMS 5, 1992, 213-215 MR 92j:54055
    • MR , vol.92 J , pp. 54055
  • 68
    • 85009775753 scopus 로고    scopus 로고
    • Williams's conjecture is false for irreducible subshifts
    • _, Williams's conjecture is false for irreducible subshifts, ERA AMS 3, 1997, 105-109 MR 98i:58081
    • (1997) ERA AMS , vol.3 , pp. 105-109
  • 69
    • 85009775753 scopus 로고    scopus 로고
    • _, Williams's conjecture is false for irreducible subshifts, ERA AMS 3, 1997, 105-109 MR 98i:58081
    • MR , vol.98 I , pp. 58081
  • 70
    • 0041156539 scopus 로고    scopus 로고
    • Williams's conjecture is false for irreducible subshifts
    • preprint from Alabama State University
    • _, Williams's conjecture is false for irreducible subshifts, preprint from Alabama State University, 1997, to appear in Annals of Mathematics
    • (1997) Annals of Mathematics
  • 72
    • 0002081150 scopus 로고    scopus 로고
    • +, Linear Algebra and Applications 145, 1991, 177-186 MR 92c:58027
    • MR , vol.92 C , pp. 58027
  • 73
    • 0002355545 scopus 로고    scopus 로고
    • Strong shift equivalence of Boolean and positive rational matrices
    • _, Strong shift equivalence of Boolean and positive rational matrices, Linear Algebra and Applications 161, 1992, 153-164 MR 93h: 15012
    • (1992) Linear Algebra and Applications , vol.161 , pp. 153-164
  • 74
    • 0002355545 scopus 로고    scopus 로고
    • _, Strong shift equivalence of Boolean and positive rational matrices, Linear Algebra and Applications 161, 1992, 153-164 MR 93h: 15012
    • MR , vol.93 H , pp. 15012
  • 75
    • 84968502774 scopus 로고    scopus 로고
    • Automorphisms of the dimension group and gyration numbers
    • K.H. Kim, F.W. Roush, and J. Wagoner, Automorphisms of the dimension group and gyration numbers, Jour. AMS 5, 1992, 191-212. MR 93h:54026
    • (1992) Jour. AMS , vol.5 , pp. 191-212
    • Kim, K.H.1    Roush, F.W.2    Wagoner, J.3
  • 76
    • 84968502774 scopus 로고    scopus 로고
    • K.H. Kim, F.W. Roush, and J. Wagoner, Automorphisms of the dimension group and gyration numbers, Jour. AMS 5, 1992, 191-212. MR 93h:54026
    • MR , vol.93 H , pp. 54026
  • 77
    • 0040562440 scopus 로고    scopus 로고
    • Characterization of inert actions on periodic points, part I and part II
    • preprint, UC Berkeley
    • _, Characterization of inert actions on periodic points, Part I and Part II, preprint, UC Berkeley, 1997, to appear in Forum Mathematicum
    • (1997) Forum Mathematicum
  • 78
    • 85009830134 scopus 로고    scopus 로고
    • Inert actions on periodic points
    • _, Inert Actions on Periodic Points, ERA AMS 3, 1997, 55-62 MR 98i:54021
    • (1997) ERA AMS , vol.3 , pp. 55-62
  • 79
    • 85009830134 scopus 로고    scopus 로고
    • _, Inert Actions on Periodic Points, ERA AMS 3, 1997, 55-62 MR 98i:54021
    • MR , vol.98 I , pp. 54021
  • 80
    • 0003210678 scopus 로고    scopus 로고
    • An introduction to Knot theory
    • Springer-Verlag
    • W.B.R. Lickorish An Introduction to Knot Theory, GTM 175, Springer-Verlag, 1997 MR 98f:57015
    • (1997) GTM , vol.175
    • Lickorish, W.B.R.1
  • 81
    • 0040562439 scopus 로고    scopus 로고
    • W.B.R. Lickorish An Introduction to Knot Theory, GTM 175, Springer-Verlag, 1997 MR 98f:57015
    • MR , vol.98 F , pp. 57015
  • 82
    • 0004229715 scopus 로고    scopus 로고
    • Springer-Verlag, Second Edition
    • J.-L. Loday, Cyclic Homology, Springer-Verlag, Second Edition, 1998 MR 98h:16014
    • (1998) Cyclic Homology
    • Loday, J.-L.1
  • 83
    • 0039969594 scopus 로고    scopus 로고
    • J.-L. Loday, Cyclic Homology, Springer-Verlag, Second Edition, 1998 MR 98h:16014
    • MR , vol.98 H , pp. 16014
  • 85
    • 0041156537 scopus 로고    scopus 로고
    • D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, 1995 MR 97a:58050
    • MR , vol.97 A , pp. 58050
  • 86
    • 0000987356 scopus 로고
    • Symbolic dynamics and connections to coding theory, automata theory and system theory
    • B. Marcus, Symbolic dynamics and connections to coding theory, automata theory and system theory, AMS Proc. Symp. Applied Math. 50, 1995, 95-108. MR 97a:58052
    • (1995) AMS Proc. Symp. Applied Math. , vol.50 , pp. 95-108
    • Marcus, B.1
  • 87
    • 0039377233 scopus 로고    scopus 로고
    • B. Marcus, Symbolic dynamics and connections to coding theory, automata theory and system theory, AMS Proc. Symp. Applied Math. 50, 1995, 95-108. MR 97a:58052
    • MR , vol.97 A , pp. 58052
  • 88
    • 0003275818 scopus 로고
    • Introduction to algebraic K-theory
    • Princeton University Press
    • J. Milnor, Introduction to Algebraic K-Theory, Annals of Mathematics Studies Number 72, Princeton University Press, 1971 MR 50:2304
    • (1971) Annals of Mathematics Studies Number , vol.72
    • Milnor, J.1
  • 89
    • 0039969592 scopus 로고    scopus 로고
    • J. Milnor, Introduction to Algebraic K-Theory, Annals of Mathematics Studies Number 72, Princeton University Press, 1971 MR 50:2304
    • MR , vol.50 , pp. 2304
  • 90
    • 0003845965 scopus 로고
    • Macmillan Company, Second Edition
    • S. MacLane and G. Birkhoff, Algebra, Macmillan Company, Second Edition, 1979 MR 80d:00002
    • (1979) Algebra
    • MacLane, S.1    Birkhoff, G.2
  • 91
    • 25544435584 scopus 로고    scopus 로고
    • S. MacLane and G. Birkhoff, Algebra, Macmillan Company, Second Edition, 1979 MR 80d:00002
    • MR , vol.80 D , pp. 00002
  • 94
    • 0002249263 scopus 로고    scopus 로고
    • 2 of split radical pairs, Journal of Pure and Applied Algebra 10, 1977, 271-294 MR 57:12485
    • MR , vol.57 , pp. 12485
  • 95
    • 0000355137 scopus 로고    scopus 로고
    • Entropy at a weight-per-symbol and an imbedding theorem for Markov chains
    • B. Marcus and S. Tuncel, Entropy at a weight-per-symbol and an imbedding theorem for Markov chains, Inventiones Mathematicae 102, 1990, 235-266. MR 91k:28023
    • (1990) Inventiones Mathematicae , vol.102 , pp. 235-266
    • Marcus, B.1    Tuncel, S.2
  • 96
    • 0000355137 scopus 로고    scopus 로고
    • B. Marcus and S. Tuncel, Entropy at a weight-per-symbol and an imbedding theorem for Markov chains, Inventiones Mathematicae 102, 1990, 235-266. MR 91k:28023
    • MR , vol.91 K , pp. 28023
  • 97
    • 84972057816 scopus 로고    scopus 로고
    • The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains
    • _, The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains, Ergodic Theory and Dynamical Systems 11, 1991, 129-180. MR 92g:28038
    • (1991) Ergodic Theory and Dynamical Systems , vol.11 , pp. 129-180
  • 98
    • 84972057816 scopus 로고    scopus 로고
    • _, The weight-per-symbol polytope and scaffolds of invariants associated with Markov chains, Ergodic Theory and Dynamical Systems 11, 1991, 129-180. MR 92g:28038
    • MR , vol.92 G , pp. 28038
  • 99
    • 84968487293 scopus 로고    scopus 로고
    • Matrices of polynomials, positivity, and finite equivalence of Markov chains
    • _ Matrices of polynomials, positivity, and finite equivalence of Markov chains, AMS Journal 6, 1993, 131-147 MR 93e:28022
    • (1993) AMS Journal , vol.6 , pp. 131-147
  • 100
    • 84968487293 scopus 로고    scopus 로고
    • _ Matrices of polynomials, positivity, and finite equivalence of Markov chains, AMS Journal 6, 1993, 131-147 MR 93e:28022
    • MR , vol.93 E , pp. 28022
  • 101
    • 0003233502 scopus 로고
    • Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov shifts
    • M. Nasu, Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov shifts, Springer Lecture Notes in Math 1342, 1988 MR 89j:54045
    • (1988) Springer Lecture Notes in Math , vol.1342
    • Nasu, M.1
  • 102
    • 0041156526 scopus 로고    scopus 로고
    • M. Nasu, Topological conjugacy for sofic systems and extensions of automorphisms of finite subsystems of topological Markov shifts, Springer Lecture Notes in Math 1342, 1988 MR 89j:54045
    • MR , vol.89 J , pp. 54045
  • 103
    • 0003323863 scopus 로고
    • Classification problems in ergodic theory
    • Cambridge University Press
    • W. Parry and S. Tuncel, Classification problems in ergodic theory, LMS Lecture Notes 67, Cambridge University Press, 1982 MR 84g:28024
    • (1982) LMS Lecture Notes , vol.67
    • Parry, W.1    Tuncel, S.2
  • 104
    • 0039969591 scopus 로고    scopus 로고
    • W. Parry and S. Tuncel, Classification problems in ergodic theory, LMS Lecture Notes 67, Cambridge University Press, 1982 MR 84g:28024
    • MR , vol.84 G , pp. 28024
  • 105
    • 0000027306 scopus 로고
    • Block coding and a zeta function for Markov chains
    • W. Parry and R.F. Williams, Block coding and a zeta function for Markov chains, Proc. LMS 35, 1977, 483-495 MR 57:6368
    • (1977) Proc. LMS , vol.35 , pp. 483-495
    • Parry, W.1    Williams, R.F.2
  • 106
    • 0039377240 scopus 로고    scopus 로고
    • W. Parry and R.F. Williams, Block coding and a zeta function for Markov chains, Proc. LMS 35, 1977, 483-495 MR 57:6368
    • MR , vol.57 , pp. 6368
  • 107
    • 0001218340 scopus 로고
    • Lectures on axiomatic topological quantum field theory
    • (edited by D. Freed and K. Uhlenbeck), IAS/Park City Mathematics Series, AMS
    • F. Quinn, Lectures on axiomatic topological quantum field theory, Geometry and Quantum Field Theory (edited by D. Freed and K. Uhlenbeck), IAS/Park City Mathematics Series, Vol. 1, AMS, 1995, 325-453 MR 96e:57021
    • (1995) Geometry and Quantum Field Theory , vol.1 , pp. 325-453
    • Quinn, F.1
  • 108
    • 0039969586 scopus 로고    scopus 로고
    • F. Quinn, Lectures on axiomatic topological quantum field theory, Geometry and Quantum Field Theory (edited by D. Freed and K. Uhlenbeck), IAS/Park City Mathematics Series, Vol. 1, AMS, 1995, 325-453 MR 96e:57021
    • MR , vol.96 E , pp. 57021
  • 109
    • 0003516946 scopus 로고
    • Algebraic K-theory and its applications
    • Springer-Verlag
    • J. Rosenberg, Algebraic K-Theory and Its Applications, GTM 147, Springer-Verlag, 1994 MR 95e:19001
    • (1994) GTM , vol.147
  • 110
    • 0041151313 scopus 로고    scopus 로고
    • J. Rosenberg, Algebraic K-Theory and Its Applications, GTM 147, Springer-Verlag, 1994 MR 95e:19001
    • MR , vol.95 E , pp. 19001
  • 111
    • 84968514104 scopus 로고    scopus 로고
    • Differential dynamical systems
    • S. Smale, Differential Dynamical Systems, BAMS, Vol. 73, No. 6, 1967, 747-847 MR 37:3598
    • (1967) BAMS , vol.73 , Issue.6 , pp. 747-847
    • Smale, S.1
  • 112
    • 84968514104 scopus 로고    scopus 로고
    • S. Smale, Differential Dynamical Systems, BAMS, Vol. 73, No. 6, 1967, 747-847 MR 37:3598
    • MR , vol.37 , pp. 3598
  • 113
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • C. Shannon, A mathematical theory of communication, Bell Sys. Tech Jour. 27, 1948, 379-423, 623-656 MR 10:133e
    • (1948) Bell Sys. Tech Jour. , vol.27 , pp. 379-423
    • Shannon, C.1
  • 114
    • 84940644968 scopus 로고    scopus 로고
    • C. Shannon, A mathematical theory of communication, Bell Sys. Tech Jour. 27, 1948, 379-423, 623-656 MR 10:133e
    • MR , vol.10
  • 115
    • 0002365908 scopus 로고
    • 3 of truncated polynomial rings
    • Springer
    • 3 of truncated polynomial rings, LNM 854, Springer, 1981 MR 82k:13016
    • (1981) LNM , vol.854
    • Stienstra, J.1
  • 116
    • 85087242596 scopus 로고    scopus 로고
    • 3 of truncated polynomial rings, LNM 854, Springer, 1981 MR 82k:13016
    • MR , vol.82 K , pp. 13016
  • 117
    • 0030460042 scopus 로고    scopus 로고
    • Augmented group systems and shifts of finite type
    • D. Silver and S. Williams, Augmented group systems and shifts of finite type, Israel Journal of Mathematics 95, 1996, 231-251 MR 98b:20045
    • (1996) Israel Journal of Mathematics , vol.95 , pp. 231-251
    • Silver, D.1    Williams, S.2
  • 118
    • 0030460042 scopus 로고    scopus 로고
    • D. Silver and S. Williams, Augmented group systems and shifts of finite type, Israel Journal of Mathematics 95, 1996, 231-251 MR 98b:20045
    • MR , vol.98 B , pp. 20045
  • 119
    • 22644448669 scopus 로고    scopus 로고
    • Knot invariants from symbolic dynamical systems
    • _ , Knot invariants from symbolic dynamical systems, to appear in Trans. AMS 351, No. 8, 1999, 3243-3265 CMP 97:17
    • (1999) Trans. AMS , vol.351 , Issue.8 , pp. 3243-3265
  • 120
    • 22644448669 scopus 로고    scopus 로고
    • _ , Knot invariants from symbolic dynamical systems, to appear in Trans. AMS 351, No. 8, 1999, 3243-3265 CMP 97:17
    • CMP , vol.97 , pp. 17
  • 121
    • 0001193165 scopus 로고
    • Faces of Markov chains and matrices of polynomials
    • AMS
    • S. Tuncel, Faces of Markov chains and matrices of polynomials, Contemporary Mathematics, Vol. 135, AMS, 1992, 391-422 MR 94m:28034
    • (1992) Contemporary Mathematics , vol.135 , pp. 391-422
    • Tuncel, S.1
  • 122
    • 0039969589 scopus 로고    scopus 로고
    • S. Tuncel, Faces of Markov chains and matrices of polynomials, Contemporary Mathematics, Vol. 135, AMS, 1992, 391-422 MR 94m:28034
    • MR , vol.94 M , pp. 28034
  • 123
    • 0000465107 scopus 로고
    • 2 des nombres duaux
    • Série A, t. 20 décembre
    • 2 des nombres duaux, C.R. Acad. Sc. Paris, Série A, t. 273 , 20 décembre 1971, 1204-1207 MR 45:252
    • (1971) C.R. Acad. Sc. Paris , vol.273 , pp. 1204-1207
    • Van Der Kallen, W.1
  • 124
    • 85087243382 scopus 로고    scopus 로고
    • 2 des nombres duaux, C.R. Acad. Sc. Paris, Série A, t. 273 , 20 décembre 1971, 1204-1207 MR 45:252
    • MR , vol.45 , pp. 252
  • 126
    • 51249179506 scopus 로고    scopus 로고
    • 2, Publ. Math. IHES, No. 65, 1987, 91-129 MR 90d:28022
    • MR , vol.90 D , pp. 28022
  • 127
    • 0002079532 scopus 로고    scopus 로고
    • Triangle identities and symmetries of a subshift affinite type
    • _, Triangle identities and symmetries of a subshift affinite type, Pacific Jour. Math. 144, 1990, 181-205 MR 91h:28017
    • (1990) Pacific Jour. Math. , vol.144 , pp. 181-205
  • 128
    • 0002079532 scopus 로고    scopus 로고
    • _, Triangle identities and symmetries of a subshift affinite type, Pacific Jour. Math. 144, 1990, 181-205 MR 91h:28017
    • MR , vol.91 H , pp. 28017
  • 129
    • 84966227566 scopus 로고    scopus 로고
    • Higher dimensional shift equivalence is the same as strong shift equivalence over the integers
    • _, Higher dimensional shift equivalence is the same as strong shift equivalence over the integers, Proc. AMS 109, 1990, 527-536 MR 90i:54088
    • (1990) Proc. AMS , vol.109 , pp. 527-536
  • 130
    • 84966227566 scopus 로고    scopus 로고
    • _, Higher dimensional shift equivalence is the same as strong shift equivalence over the integers, Proc. AMS 109, 1990, 527-536 MR 90i:54088
    • MR , vol.90 I , pp. 54088
  • 131
    • 0002082607 scopus 로고    scopus 로고
    • Eventual finite order generation for the kernel of the dimension group representation
    • _, Eventual finite order generation for the kernel of the dimension group representation, Trans. AMS 317, 1990, 331-350 MR 91a:54055
    • (1990) Trans. AMS , vol.317 , pp. 331-350
  • 132
    • 0002082607 scopus 로고    scopus 로고
    • _, Eventual finite order generation for the kernel of the dimension group representation, Trans. AMS 317, 1990, 331-350 MR 91a:54055
    • MR , vol.91 A , pp. 54055
  • 133
    • 0002081933 scopus 로고
    • Classification of subshifts of finite type revisited
    • AMS
    • _, Classification of subshifts of finite type revisited, Contemporary Mathematics, Vol. 135, AMS, 1992, 423-436 MR 93m:20004
    • (1992) Contemporary Mathematics , vol.135 , pp. 423-436
  • 134
    • 0039377231 scopus 로고    scopus 로고
    • _, Classification of subshifts of finite type revisited, Contemporary Mathematics, Vol. 135, AMS, 1992, 423-436 MR 93m:20004
    • MR , vol.93 M , pp. 20004
  • 135
    • 0002065958 scopus 로고    scopus 로고
    • 2
    • 2, Advances of Mathematics, Vol. 71, No. 2, 1988, 133-185 MR 90j:46059
    • (1988) Advances of Mathematics , vol.71 , Issue.2 , pp. 133-185
  • 136
    • 0002065958 scopus 로고    scopus 로고
    • 2, Advances of Mathematics, Vol. 71, No. 2, 1988, 133-185 MR 90j:46059
    • MR , vol.90 J , pp. 46059
  • 137
    • 0040562436 scopus 로고    scopus 로고
    • 2 of the dual numbers
    • preprint from UC Berkeley
    • 2 of the dual numbers, preprint from UC Berkeley, 1998, to appear in Jour. Reine Angew. Math.
    • (1998) Jour. Reine Angew. Math.
  • 138
    • 0001745950 scopus 로고
    • Classification of subshifts of finite type
    • Errata ibid. 99, 1974, 380-381
    • R.F. Williams, Classification of subshifts of finite type, Annals of Math.(2) 98, 1973, 120-153; Errata ibid. 99, 1974, 380-381. MR 48:9769
    • (1973) Annals of Math. , vol.98 , Issue.2 , pp. 120-153
    • Williams, R.F.1
  • 139
    • 0041156532 scopus 로고    scopus 로고
    • R.F. Williams, Classification of subshifts of finite type, Annals of Math.(2) 98, 1973, 120-153; Errata ibid. 99, 1974, 380-381. MR 48:9769
    • MR , vol.48 , pp. 9769
  • 140
    • 0002065960 scopus 로고
    • Shift equivalence of matrices in GL(2,Z)
    • AMS
    • _, Shift equivalence of matrices in GL(2,Z), Cont. Math., Vol. 135, AMS, 1992, 445-451 MR 93k:58183
    • (1992) Cont. Math. , vol.135 , pp. 445-451
  • 141
    • 0039969588 scopus 로고    scopus 로고
    • _, Shift equivalence of matrices in GL(2,Z), Cont. Math., Vol. 135, AMS, 1992, 445-451 MR 93k:58183
    • MR , vol.93 K , pp. 58183
  • 143
    • 0039377235 scopus 로고    scopus 로고
    • _, Classification of 1-dimensional attractors, Global Analysis, Proceedings of the Symposium on Pure Mathematics 14, AMS, 1970, 341-361 MR 42:1134
    • MR , vol.42 , pp. 1134


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.