메뉴 건너뛰기




Volumn 77, Issue 4, 2002, Pages 718-745

Rigidity of measurable structure for ℤd-actions by automorphisms of a torus

Author keywords

Commuting hyperbolic toral automorphisms; Isomorphism rigidity of d actions

Indexed keywords


EID: 0036951258     PISSN: 00102571     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00012439     Document Type: Article
Times cited : (59)

References (30)
  • 1
    • 0000458958 scopus 로고
    • Entropy, a complete metric invariant for automorphisms of the torus
    • R. L. Adler and B. Weiss, Entropy, a complete metric invariant for automorphisms of the torus, Proc. Nat. Acad. Sci. 57 (1967), 1573-1576.
    • (1967) Proc. Nat. Acad. Sci. , vol.57 , pp. 1573-1576
    • Adler, R.L.1    Weiss, B.2
  • 2
    • 84967780444 scopus 로고
    • Multi-invariant sets on tori
    • D. Berend, Multi-invariant sets on tori, Trans. Amer. Math. Soc. 280 (1983), 509-532.
    • (1983) Trans. Amer. Math. Soc. , vol.280 , pp. 509-532
    • Berend, D.1
  • 5
    • 0004131235 scopus 로고
    • Chelsea, New York
    • F. R. Gantmacher, Theory of matrices, vol. 1, Chelsea, New York, 1959; vol. 2, Chelsea, New York, 1960.
    • (1959) Theory of Matrices , vol.1
    • Gantmacher, F.R.1
  • 6
    • 0004131235 scopus 로고
    • Chelsea, New York
    • F. R. Gantmacher, Theory of matrices, vol. 1, Chelsea, New York, 1959; vol. 2, Chelsea, New York, 1960.
    • (1960) Theory of Matrices , vol.2
  • 7
    • 0000794504 scopus 로고
    • On automorphisms of compact groups
    • P. R. Halmos, On automorphisms of compact groups, Bull. Amer. Math. Soc. 49 (1943), 619-624.
    • (1943) Bull. Amer. Math. Soc. , vol.49 , pp. 619-624
    • Halmos, P.R.1
  • 9
    • 84972556252 scopus 로고
    • d actions by automorphisms of compact abelian groups
    • d actions by automorphisms of compact abelian groups, Pacific Jour. Math. 170 (1995), 105-142.
    • (1995) Pacific Jour. Math. , vol.170 , pp. 105-142
    • Katok, A.1    Schmidt, K.2
  • 10
    • 51249167977 scopus 로고
    • First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
    • A. Katok and R. J. Spatzier, First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity, Publ. Math. IHES 79 (1994), 131-156.
    • (1994) Publ. Math. IHES , vol.79 , pp. 131-156
    • Katok, A.1    Spatzier, R.J.2
  • 11
    • 0000529772 scopus 로고
    • Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions
    • A. Katok and R. J. Spatzier, Subelliptic estimates of polynomial differential operators and applications to rigidity of abelian actions, Math. Res. Lett. 1 (1994), 193-202.
    • (1994) Math. Res. Lett. , vol.1 , pp. 193-202
    • Katok, A.1    Spatzier, R.J.2
  • 12
    • 0030520144 scopus 로고    scopus 로고
    • Invariant measures for higher rank hyperbolic abelian actions
    • Corrections: Ergod. Th. & Dynam. Sys. 18 (1998), 503-507
    • A. Katok and R. J. Spatzier, Invariant measures for higher rank hyperbolic abelian actions, Ergod. Th. & Dynam. Sys. 16 (1996), 751-778; Corrections: Ergod. Th. & Dynam. Sys. 18 (1998), 503-507.
    • (1996) Ergod. Th. & Dynam. Sys. , vol.16 , pp. 751-778
    • Katok, A.1    Spatzier, R.J.2
  • 13
    • 0000983709 scopus 로고    scopus 로고
    • Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions
    • A. Katok and R. J. Spatzier, Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions, Proc. Steklov Inst. Math. 216 (1997), 287-314.
    • (1997) Proc. Steklov Inst. Math. , vol.216 , pp. 287-314
    • Katok, A.1    Spatzier, R.J.2
  • 14
    • 0001637921 scopus 로고    scopus 로고
    • Coding of closed geodesics after gauss and morse
    • S. Katok, Coding of closed geodesics after Gauss and Morse, Geom. Dedicata 63 (1996), 123-145.
    • (1996) Geom. Dedicata , vol.63 , pp. 123-145
    • Katok, S.1
  • 15
    • 51249188998 scopus 로고
    • n are bernoulli shifts
    • n are Bernoulli shifts, Israel J. Math. 10 (1971), 186-195.
    • (1971) Israel J. Math. , vol.10 , pp. 186-195
    • Katznelson, I.1
  • 18
    • 0000522910 scopus 로고
    • A correspondence between classes of ideals and classes of matrices
    • Latimer and C. C. MacDuffee, A correspondence between classes of ideals and classes of matrices, Ann. Math. 74 (1933), 313-316.
    • (1933) Ann. Math. , vol.74 , pp. 313-316
    • Latimer1    Macduffee, C.C.2
  • 19
    • 0000635276 scopus 로고
    • Mahler measure and entropy for commuting automorphisms of compact groups
    • D. Lind, K. Schmidt and T. Ward, Mahler measure and entropy for commuting automorphisms of compact groups, Invent. Math. 101 (1990), 593-629.
    • (1990) Invent. Math. , vol.101 , pp. 593-629
    • Lind, D.1    Schmidt, K.2    Ward, T.3
  • 20
    • 0000768820 scopus 로고
    • Bernoulli shifts with the same entropy are isomorphic
    • D. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Adv. Math. 4 (1970), 337-352.
    • (1970) Adv. Math. , vol.41 , pp. 337-352
    • Ornstein, D.1
  • 21
    • 0001146168 scopus 로고
    • Rigidity of horocycle flows
    • M. Ratner, Rigidity of horocycle flows, Ann. Math. 115, (1982), 597-614.
    • (1982) Ann. Math. , vol.115 , pp. 597-614
    • Ratner, M.1
  • 22
    • 0000012701 scopus 로고
    • Factors of horocycle flows
    • M. Ratner, Factors of horocycle flows, Ergod. Th. & Dynam. Sys. 2 (1982), 465-489.
    • (1982) Ergod. Th. & Dynam. Sys. , vol.2 , pp. 465-489
    • Ratner, M.1
  • 23
    • 0001349056 scopus 로고
    • Horocycle flows, joinings and rigidity of products
    • M. Ratner, Horocycle flows, joinings and rigidity of products, Ann. Math. 118 (1983), 277-313.
    • (1983) Ann. Math. , vol.118 , pp. 277-313
    • Ratner, M.1
  • 25
    • 0001240275 scopus 로고
    • Automorphisms of compact abelian groups and affine varieties
    • K. Schmidt, Automorphisms of compact abelian groups and affine varieties, Proc. London Math. Soc. 61 (1990), 480-496.
    • (1990) Proc. London Math. Soc. , vol.61 , pp. 480-496
    • Schmidt, K.1
  • 27
    • 0012491921 scopus 로고    scopus 로고
    • d-actions, Smooth ergodic theory and its applications
    • Seattle, WA, 1999, Amer. Math. Soc., Providence, RI
    • d-actions, Smooth ergodic theory and its applications (Seattle, WA, 1999), 661-676, Proc. Sympos. Pure Math. 69, Amer. Math. Soc., Providence, RI, 2001.
    • (2001) Proc. Sympos. Pure Math. , vol.69 , pp. 661-676
    • Schmidt, K.1
  • 28
    • 0012491922 scopus 로고    scopus 로고
    • First cohomology group, mixing and minimal sets of commutative group of algebraic action on torus
    • Dynamical systems, 7, (New York)
    • A. Starkov, First cohomology group, mixing and minimal sets of commutative group of algebraic action on torus, Dynamical systems, 7, J. Math. Sci. (New York) 95 (1999), no. 5, 2576-2582.
    • (1999) J. Math. Sci. , vol.95 , Issue.5 , pp. 2576-2582
    • Starkov, A.1
  • 29
    • 0007245754 scopus 로고
    • Introduction into connections between algebraic number theory and integral matrices
    • Appendix to: H. Cohn, Springer, New York
    • O. Taussky, Introduction into connections between algebraic number theory and integral matrices, Appendix to: H. Cohn, A classical invitation to algebraic numbers and class field, Springer, New York, 1978.
    • (1978) A Classical Invitation to Algebraic Numbers and Class Field
    • Taussky, O.1
  • 30
    • 84967774620 scopus 로고
    • Conjugacy classes of hyperbolic matrices in SL(n, ℤ) and ideal classes in an order
    • D. I. Wallace, Conjugacy classes of hyperbolic matrices in SL(n, ℤ) and ideal classes in an order, Trans. Amer. Math. Soc. 283 (1984), 177-184.
    • (1984) Trans. Amer. Math. Soc. , vol.283 , pp. 177-184
    • Wallace, D.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.