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Volumn 21, Issue 2, 1999, Pages 161-191

Geometric models for quasicrystals I. Delone sets of finite type

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EID: 0033478409     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009413     Document Type: Article
Times cited : (119)

References (79)
  • 1
    • 0013431406 scopus 로고    scopus 로고
    • A guide to mathematical quasicrystals
    • J. B. Suck, M. Schrieber, and P. Häussier, Eds., Springer-Verlag: Berlin, in press
    • M. Baake, A guide to mathematical quasicrystals, in: Quasicrystals (J. B. Suck, M. Schrieber, and P. Häussier, Eds.), Springer-Verlag: Berlin, 1999, in press.
    • (1999) Quasicrystals
    • Baake, M.1
  • 2
    • 0040180270 scopus 로고
    • Geometric aspects of tiling and equivalence concepts
    • C. Janot and R. Mossieri, Eds., World Scientific: Singapore
    • M. Baake and M. Schlottmann, Geometric aspects of tiling and equivalence concepts, in: Proceedings of the 5th International Conference on Quasicrystals (C. Janot and R. Mossieri, Eds.), World Scientific: Singapore, 1995, pp. 15-21.
    • (1995) Proceedings of the 5th International Conference on Quasicrystals , pp. 15-21
    • Baake, M.1    Schlottmann, M.2
  • 3
    • 36149029722 scopus 로고
    • Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability
    • M. Baake, M. Schlottmann, and P. D. Jarvis, Quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability, J. Phys. A 24 (1991), 4637-4654.
    • (1991) J. Phys. A , vol.24 , pp. 4637-4654
    • Baake, M.1    Schlottmann, M.2    Jarvis, P.D.3
  • 5
    • 0038163729 scopus 로고
    • Quasiperiodicity: Local and global aspects
    • Group-Theoretical Methods in Physics (V. V Dodonov and V. I. Man'ko, Eds.), Springer-Verlag: New York
    • L. Danzer, Quasiperiodicity: local and global aspects, in: Group-Theoretical Methods in Physics (V. V Dodonov and V. I. Man'ko, Eds.), Lecture Notes in Physics, Vol. 382, Springer-Verlag: New York, 1990, pp. 561-572.
    • (1990) Lecture Notes in Physics , vol.382 , pp. 561-572
    • Danzer, L.1
  • 7
    • 0040889246 scopus 로고    scopus 로고
    • Delone graphs; some species and local rules
    • R. V. Moody, Ed., Kluwer: Dordrecht
    • L. Danzer and N. Dolbilin, Delone graphs; some species and local rules, in: The Mathematics of Long-Range Aperiodic Order (R. V. Moody, Ed.), Kluwer: Dordrecht, 1997, pp. 98-114.
    • (1997) The Mathematics of Long-range Aperiodic Order , pp. 98-114
    • Danzer, L.1    Dolbilin, N.2
  • 12
    • 24944556383 scopus 로고
    • The diffraction pattern of projected structures
    • V. Elser, The diffraction pattern of projected structures, Acta Cryst. Sect. A 42 (1986), 36-43.
    • (1986) Acta Cryst. Sect. A , vol.42 , pp. 36-43
    • Elser, V.1
  • 13
    • 0011973816 scopus 로고    scopus 로고
    • Substitution dynamical systems: Algebraic characterization of eigenvalues
    • S. Ferenczi, C. Mauduit, and A. Nogueira, Substitution dynamical systems: algebraic characterization of eigenvalues, Ann. Sci. École Norm. Sup. 29 (1996), 519-533.
    • (1996) Ann. Sci. École Norm. Sup. , vol.29 , pp. 519-533
    • Ferenczi, S.1    Mauduit, C.2    Nogueira, A.3
  • 14
    • 0001465710 scopus 로고
    • Voronoi diagrams and Delaunay triangulations
    • F. K. Hwang and D. Z. Du, Eds., World Scientific: Singapore
    • S. Fortune, Voronoi diagrams and Delaunay triangulations, in: Computing in Euclidean Geometry, 2nd edn. (F. K. Hwang and D. Z. Du, Eds.), World Scientific: Singapore, 1995, pp. 225-265.
    • (1995) Computing in Euclidean Geometry, 2nd Edn. , pp. 225-265
    • Fortune, S.1
  • 15
    • 0002654690 scopus 로고    scopus 로고
    • Voronoi diagrams and Delaunay triangulations
    • J. E. Goodman and J. O'Rourke, Eds., CRC Press: Baton Rouge, LA
    • S. Fortune, Voronoi diagrams and Delaunay triangulations, in: Handbook of Discrete and Computational Geometry (J. E. Goodman and J. O'Rourke, Eds.), CRC Press: Baton Rouge, LA, 1997, pp. 377-388.
    • (1997) Handbook of Discrete and Computational Geometry , pp. 377-388
    • Fortune, S.1
  • 16
    • 33646727744 scopus 로고
    • Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation
    • H. Furstenberg, Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Systems Theory 1 (1967), 1-49.
    • (1967) Math. Systems Theory , vol.1 , pp. 1-49
    • Furstenberg, H.1
  • 17
    • 0001061322 scopus 로고
    • Binary tiling quasicrystals and matching rules
    • F. Gähler, M. Baake, and M. Schlottman, Binary tiling quasicrystals and matching rules, Phys. Rev. B 50 (1994), 12458-12467.
    • (1994) Phys. Rev. B , vol.50 , pp. 12458-12467
    • Gähler, F.1    Baake, M.2    Schlottman, M.3
  • 18
    • 0037823560 scopus 로고    scopus 로고
    • The diffraction pattern of self-similar tilings
    • R. V. Moody, Ed., Kluwer: Dordrecht
    • F. Gähler and R. Klitzing, The diffraction pattern of self-similar tilings, in: The Mathematics of Long-Range Aperiodic Order (R. V. Moody, Ed.), Kluwer: Dordrecht, 1997, pp. 141-174.
    • (1997) The Mathematics of Long-range Aperiodic Order , pp. 141-174
    • Gähler, F.1    Klitzing, R.2
  • 19
    • 0000569432 scopus 로고
    • Delaunay systems
    • R. V. Galiulin, Delaunay systems, Soviet Phys. Cryst. 25(5) (1980), 517-520.
    • (1980) Soviet Phys. Cryst. , vol.25 , Issue.5 , pp. 517-520
    • Galiulin, R.V.1
  • 20
    • 0030151441 scopus 로고    scopus 로고
    • Quasicrystalline materials
    • A. I. Goldman et al., Quasicrystalline materials. Amer. Sci. 84 (1996), 230-241.
    • (1996) Amer. Sci. , vol.84 , pp. 230-241
    • Goldman, A.I.1
  • 22
    • 36149029485 scopus 로고
    • Random tilings with quasicrystal order: Transfer-matrix approach
    • C. Henley, Random tilings with quasicrystal order: transfer-matrix approach, J. Phys. A 21 (1988), 1649-1677.
    • (1988) J. Phys. A , vol.21 , pp. 1649-1677
    • Henley, C.1
  • 23
    • 0002754401 scopus 로고
    • Random tiling models
    • D. P. DiVincenzo and P. J. Steinhardt, Eds., World Scientific: Singapore
    • C. Henley, Random tiling models, in: Quasicrystals: The State of the Art (D. P. DiVincenzo and P. J. Steinhardt, Eds.), World Scientific: Singapore, 1991, pp. 429-524.
    • (1991) Quasicrystals: The State of the Art , pp. 429-524
    • Henley, C.1
  • 24
    • 21844524319 scopus 로고
    • On diffraction by aperiodic structures
    • A Hof, On diffraction by aperiodic structures, Comm. Math. Phys. 169 (1995), 25-43.
    • (1995) Comm. Math. Phys. , vol.169 , pp. 25-43
    • Hof, A.1
  • 25
    • 0030186880 scopus 로고    scopus 로고
    • On a "structure intermediate between quasiperiodic and random,"
    • A. Hof, On a "Structure Intermediate Between Quasiperiodic and Random," J. Statist. Phys. 84 (1996), 309-320.
    • (1996) J. Statist. Phys. , vol.84 , pp. 309-320
    • Hof, A.1
  • 26
    • 0002492934 scopus 로고    scopus 로고
    • Diffraction by aperiodic structures
    • R. V. Moody, Ed., Kluwer: Dordrecht
    • A. Hof, Diffraction by aperiodic structures, in: The Mathematics of Long-Range Aperiodic Order (R. V. Moody, Ed.), Kluwer: Dordrecht, 1997, pp. 239-268.
    • (1997) The Mathematics of Long-range Aperiodic Order , pp. 239-268
    • Hof, A.1
  • 27
  • 28
    • 0013557146 scopus 로고
    • Matching rules for quasicrystalline tilings
    • D. P. DiVincenzo and P. J. Steinhardt, Eds., World Scientific: Singapore
    • K. Ingersent, Matching rules for quasicrystalline tilings, in: Quasicrystals - The State of the Art (D. P. DiVincenzo and P. J. Steinhardt, Eds.), World Scientific: Singapore, 1991, pp. 185-212.
    • (1991) Quasicrystals - The State of the Art , pp. 185-212
    • Ingersent, K.1
  • 30
    • 0023418698 scopus 로고
    • Incommensurability in crystals
    • T. Janssen and A. Janner, Incommensurability in crystals, Adv. in Phys. 36 (1987), 519-624.
    • (1987) Adv. in Phys. , vol.36 , pp. 519-624
    • Janssen, T.1    Janner, A.2
  • 31
    • 0002189446 scopus 로고
    • A geometric approach to quasiperiodic tilings
    • A. Katz, M. Duneau, and C. Oguey, A geometric approach to quasiperiodic tilings. Comm. Math. Phys. 118 (1988), 99-118.
    • (1988) Comm. Math. Phys. , vol.118 , pp. 99-118
    • Katz, A.1    Duneau, M.2    Oguey, C.3
  • 32
    • 0000000958 scopus 로고
    • Self-replicating tilings
    • P. Walters, Ed. American Mathematical Society: Providence, RI
    • R. Kenyon, Self-replicating tilings, in: Symbolic Dynamics and Its Applications (P. Walters, Ed.) American Mathematical Society: Providence, RI, 1992, pp. 239-264.
    • (1992) Symbolic Dynamics and Its Applications , pp. 239-264
    • Kenyon, R.1
  • 33
    • 51249169419 scopus 로고
    • Inflationary tilings with similarity structure
    • R. Kenyon, Inflationary tilings with similarity structure, Comment. Math. Helv: 69 (1994), 169-198.
    • (1994) Comment. Math. Helv , vol.69 , pp. 169-198
    • Kenyon, R.1
  • 34
    • 0030556295 scopus 로고    scopus 로고
    • The construction of self-similar tilings
    • R. Kenyon The construction of self-similar tilings, Geom. Funct. Anal. 6 (1996), 471-488.
    • (1996) Geom. Funct. Anal. , vol.6 , pp. 471-488
    • Kenyon, R.1
  • 35
    • 84922427981 scopus 로고
    • Representation of certain self-similar quasiperiodic tilings with perfect matching rules by discrete point sets
    • R. Klitzing and M. Baake, Representation of certain self-similar quasiperiodic tilings with perfect matching rules by discrete point sets, J. Phys. France 4 (1994), 893-904.
    • (1994) J. Phys. France , vol.4 , pp. 893-904
    • Klitzing, R.1    Baake, M.2
  • 36
    • 0007882984 scopus 로고
    • Structure factor of ID systems (superlattices) based on two-letter substitution rules: I. Bragg peaks
    • M. Kolàr B. Iochum, and L. Raymond, Structure factor of ID systems (superlattices) based on two-letter substitution rules: I. Bragg peaks, J. Phys. A 26 (1993), 7343-7366.
    • (1993) J. Phys. A , vol.26 , pp. 7343-7366
    • Kolàr, M.1    Iochum, B.2    Raymond, L.3
  • 37
    • 84944818724 scopus 로고
    • m obtained by projection
    • Erratum, Acta Cryst. Sect. A 41(1985), 619
    • m obtained by projection, Acta. Cryst. Sect. A 40 (1984), 580-587. (Erratum, Acta Cryst. Sect. A 41(1985), 619.)
    • (1984) Acta. Cryst. Sect. A , vol.40 , pp. 580-587
    • Kramer, P.1    Neri, R.2
  • 38
    • 0030210212 scopus 로고    scopus 로고
    • Meyer's concept of quasicrystal and quasiregular sets
    • J. C. Lagarias, Meyer's concept of quasicrystal and quasiregular sets, Comm. Math. Phys. 179 (1996),
    • (1996) Comm. Math. Phys. , vol.179
    • Lagarias, J.C.1
  • 39
    • 84922442389 scopus 로고    scopus 로고
    • Geometric models for quasicrystals, II. Local rules under isometries
    • to appear
    • J. C. Lagarias, Geometric models for quasicrystals, II. Local rules under isometries, Discrete Comput. Geom., to appear.
    • Discrete Comput. Geom.
    • Lagarias, J.C.1
  • 41
    • 38248998759 scopus 로고
    • A polyomino tiling problem of Thurston and its configurational entropy
    • J. C. Lagarias and D. S. Romano, A polyomino tiling problem of Thurston and its configurational entropy, J. Combin. Theory Ser. A 63 (1993), 338-358.
    • (1993) J. Combin. Theory Ser. A , vol.63 , pp. 338-358
    • Lagarias, J.C.1    Romano, D.S.2
  • 43
    • 0000072605 scopus 로고
    • Quasicrystals: A new class of ordered structures
    • D. Levine and P. J. Steinhardt, Quasicrystals: a new class of ordered structures, Phys. Rev. Lett. 53 (1984), 2477-2480.
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 2477-2480
    • Levine, D.1    Steinhardt, P.J.2
  • 44
    • 33750969559 scopus 로고
    • Quasicrystals, I. Definition and structure
    • D. Livine and P. J. Steinhardt, Quasicrystals, I. Definition and structure, Phys. Rev. B 34 (1986), 596-616.
    • (1986) Phys. Rev. B , vol.34 , pp. 596-616
    • Livine, D.1    Steinhardt, P.J.2
  • 45
    • 84922419661 scopus 로고
    • Local rules for quasicrystals
    • L. S. Levitov, Local rules for quasicrystals, Comm. Math. Phys. 118 (1988), 37-100.
    • (1988) Comm. Math. Phys. , vol.118 , pp. 37-100
    • Levitov, L.S.1
  • 46
    • 0010724358 scopus 로고
    • The entropies of topological Markov shifts and a related class of algebraic integers
    • D. A. Lind, The entropies of topological Markov shifts and a related class of algebraic integers, Ergodic Theory Dynamical Systems 40 (1984), 283-300.
    • (1984) Ergodic Theory Dynamical Systems , vol.40 , pp. 283-300
    • Lind, D.A.1
  • 47
    • 38249010974 scopus 로고
    • Matrices of Perron numbers
    • D. A. Lind, Matrices of Perron numbers, J. Number Theory 40 (1992), 211-217.
    • (1992) J. Number Theory , vol.40 , pp. 211-217
    • Lind, D.A.1
  • 50
    • 0003861527 scopus 로고
    • Quasicrystallography is better in Fourier space
    • D. P. DiVincenzo and P. J. Steinhardt, Eds., World Scientific: Singapore
    • N. D. Mermin, Quasicrystallography is better in Fourier space, in: Quasicrystals: The State of the Art (D. P. DiVincenzo and P. J. Steinhardt, Eds.), World Scientific: Singapore, 1991, pp. 133-183.
    • (1991) Quasicrystals: The State of the Art , pp. 133-183
    • Mermin, N.D.1
  • 51
    • 0038241316 scopus 로고
    • Nombres de pisot, nombres de salem, et analyse harmonique
    • Springer-Verlag: Berlin
    • Y. Meyer, Nombres de Pisot, Nombres de Salem, et analyse harmonique, Lecture Notes in Mathematics, No. 117, Springer-Verlag: Berlin, 1970.
    • (1970) Lecture Notes in Mathematics , vol.117
    • Meyer, Y.1
  • 53
    • 0037848342 scopus 로고
    • Quasicrystals, diophantine approximation and algebraic numbers
    • F. Axel and D. Gratis, Eds., Les Editions de Physique, Springer-Verlag: Paris
    • Y. Meyer, Quasicrystals, Diophantine approximation and algebraic numbers, in: Beyond Quasicrystals (F. Axel and D. Gratis, Eds.), Les Editions de Physique, Springer-Verlag: Paris, 1995, pp. 3-16.
    • (1995) Beyond Quasicrystals , pp. 3-16
    • Meyer, Y.1
  • 54
    • 0037486032 scopus 로고
    • Meyer sets and the finite generation of quasicrystals
    • P. Gruber, Ed. Plenum: London.
    • R. V. Moody, Meyer sets and the finite generation of quasicrystals, in: Symmetries in Science VIII (P. Gruber, Ed.) Plenum: London. 1995.
    • (1995) Symmetries in Science VIII
    • Moody, R.V.1
  • 55
    • 0002421044 scopus 로고    scopus 로고
    • Meyer sets and their duals
    • R. V. Moody, Ed., Kluwer: Dordrecht
    • R. V. Moody, Meyer sets and their duals, in: The Mathematics of Long-Range Aperiodic Order (R. V. Moody, Ed.), Kluwer: Dordrecht, 1997, pp. 403-442.
    • (1997) The Mathematics of Long-range Aperiodic Order , pp. 403-442
    • Moody, R.V.1
  • 57
    • 0038580083 scopus 로고
    • Colourings of quasicrystals
    • R. V. Moody and J. Patera, Colourings of quasicrystals, Canad. J. Phys. 72 (1995), 442-452.
    • (1995) Canad. J. Phys. , vol.72 , pp. 442-452
    • Moody, R.V.1    Patera, J.2
  • 59
    • 0002189446 scopus 로고
    • A geometric approach to quasiperiodic tilings
    • C. Oguey, M. Duneau, and A. Katz, A geometric approach to quasiperiodic tilings, Comm. Math. Phys. 118 (1988), 99-118.
    • (1988) Comm. Math. Phys. , vol.118 , pp. 99-118
    • Oguey, C.1    Duneau, M.2    Katz, A.3
  • 60
    • 0040295028 scopus 로고
    • Quasicrystallographic groups in the sense of Novikov
    • S. A. Piunikhin, Quasicrystallographic groups in the sense of Novikov, Mat. Zametki 47(5) (1990), 81-87 [Math. Notes 47 (1990), 478-482].
    • (1990) Mat. Zametki , vol.47 , Issue.5 , pp. 81-87
    • Piunikhin, S.A.1
  • 61
    • 0039110942 scopus 로고
    • S. A. Piunikhin, Quasicrystallographic groups in the sense of Novikov, Mat. Zametki 47(5) (1990), 81-87 [Math. Notes 47 (1990), 478-482].
    • (1990) Math. Notes , vol.47 , pp. 478-482
  • 62
    • 84922451442 scopus 로고    scopus 로고
    • paper in preparation
    • P. A. B. Pleasants, paper in preparation.
    • Pleasants, P.A.B.1
  • 63
    • 85072827016 scopus 로고
    • Substitution dynamical systems - Spectral analysis
    • Springer-Verlag: New York
    • M. Queffelec, Substitution Dynamical Systems - Spectral Analysis, Lecture Notes in Mathematics, Vol. 1294. Springer-Verlag: New York, 1987.
    • (1987) Lecture Notes in Mathematics , vol.1294
    • Queffelec, M.1
  • 64
    • 0000704080 scopus 로고
    • Low temperature and the origin of crystalline symmetry
    • C. Radin, Low temperature and the origin of crystalline symmetry. Internal. J. Mod. Phys. B 1 (1987), 1157-1191.
    • (1987) Internal. J. Mod. Phys. B , vol.1 , pp. 1157-1191
    • Radin, C.1
  • 65
    • 0009272116 scopus 로고
    • Disordered ground states for classical lattice models
    • C. Radin, Disordered ground states for classical lattice models, Rev. Math. Phys. 3 (1991), 125-135.
    • (1991) Rev. Math. Phys. , vol.3 , pp. 125-135
    • Radin, C.1
  • 66
    • 84967707576 scopus 로고
    • Global order from local sources
    • C. Radin, Global order from local sources, Bull. Amer. Math. Soc. 25 (1991), 335-364.
    • (1991) Bull. Amer. Math. Soc. , vol.25 , pp. 335-364
    • Radin, C.1
  • 67
    • 0040295031 scopus 로고
    • n versus Ζ actions for systems of finite type
    • American Mathematical Society: Providence, RI
    • n Versus Ζ Actions for Systems of Finite Type, Contemporary Mathematics, Vol. 135 American Mathematical Society: Providence, RI, 1992, pp. 339-342.
    • (1992) Contemporary Mathematics , vol.135 , pp. 339-342
    • Radin, C.1
  • 68
    • 0009234666 scopus 로고    scopus 로고
    • The dynamical theory of tilings and quasicrystallography
    • d Actions (M. Pollicott and K. Schmidt, Eds.), Cambridge University Press: Cambridge
    • d Actions (M. Pollicott and K. Schmidt, Eds.), London Mathematical Society Lecture Notes, Vol. 228, Cambridge University Press: Cambridge, 1996, pp. 451-473.
    • (1996) London Mathematical Society Lecture Notes , vol.228 , pp. 451-473
    • Robinson E.A., Jr.1
  • 69
    • 0004279601 scopus 로고
    • Cambridge University Press: Cambridge
    • C. A. Rogers, Packing and Covering, Cambridge University Press: Cambridge, 1964.
    • (1964) Packing and Covering
    • Rogers, C.A.1
  • 71
    • 0001291170 scopus 로고    scopus 로고
    • Cut and project sets in locally compact abelian groups
    • Fields Institute Communications, American Mathematical Society, Providence, RI, to appear
    • M. Schlottmann, Cut and project sets in locally compact abelian groups, Proceedings of the Workshop on Aperiodic Order, Fields Institute Communications, American Mathematical Society, Providence, RI, to appear.
    • Proceedings of the Workshop on Aperiodic Order
    • Schlottmann, M.1
  • 73
    • 35949020127 scopus 로고
    • Quasicrystals, II. Unit cell configurations
    • J. Socolar and P. J. Steinhardt, Quasicrystals, II. Unit cell configurations, Phys. Rev. B 34 (1986), 617-647.
    • (1986) Phys. Rev. B , vol.34 , pp. 617-647
    • Socolar, J.1    Steinhardt, P.J.2
  • 74
    • 0001360360 scopus 로고
    • On the spectral theory of adic transformations
    • B. Solomyak, On the spectral theory of adic transformations. Adv. Soviet Math. 9 (1992), 217-230.
    • (1992) Adv. Soviet Math. , vol.9 , pp. 217-230
    • Solomyak, B.1
  • 76
    • 0040350273 scopus 로고    scopus 로고
    • Nonperiodicity implies unique composition for self-similar translationally finite tilings
    • B. Solomyak, Nonperiodicity implies unique composition for self-similar translationally finite tilings, Discrete Comput. Geom. 20 (1998), 265-279.
    • (1998) Discrete Comput. Geom. , vol.20 , pp. 265-279
    • Solomyak, B.1
  • 79
    • 0011414005 scopus 로고
    • Groups, tilings and finite state automata
    • Boulder, American Mathematical Society, Providence, RI, 1989
    • W. Thurston, Groups, Tilings and Finite State Automata, AMS Colloquium Lecture Notes, Boulder, 1989, American Mathematical Society, Providence, RI, 1989.
    • (1989) AMS Colloquium Lecture Notes
    • Thurston, W.1


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