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2000 | 165 | 2 | 125-138
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Inverse limit spaces of post-critically finite tent maps

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Let (I,T) be the inverse limit space of a post-critically finite tent map. Conditions are given under which these inverse limit spaces are pairwise nonhomeomorphic. This extends results of Barge & Diamond [2].
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  • Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, U.S.A., bruin@its.caltech.edu
Bibliografia
  • [1] C. Bandt, Composants of the horseshoe, Fund. Math.144 (1994), 231-241.
  • [2] M. Barge and B. Diamond, Homeomorphisms of inverse limit spaces of one-dimensional maps, ibid.146 (1995), 171-187.
  • [3] M. Barge and S. Holte, Nearly one-dimensional Hénon attractors and inverse limits, Nonlinearity8 (1995), 29-42.
  • [4] M. Barge and W. Ingram, Inverse limits on [0,1] using logistic bonding maps, Topology Appl.72 (1996), 159-172.
  • [5] M. Barge and J. Martin, Endpoints of inverse limit spaces and dynamics, in: Continua with the Houston Problem Book, Lecture Notes in Pure and Appl. Math. 170, Marcel Dekker, New York, 1995, 165-182.
  • [6] K. Brucks and B. Diamond, A symbolic representation of inverse limit spaces for a class of unimodal maps, ibid., 207-226.
  • [7] H. Bruin, Planar embeddings of inverse limit spaces of unimodal maps, Topology Applications96 (1999), 191-208.
  • [8] A. Douady et J. Hubbard, Étude dynamique des polynômes complexes, partie I, Publ. Math. Orsay 85-04, 1984.
  • [9] F. Durand, A generalization of Cobham's Theorem, Theory Comput. Syst.31 (1998), 169-185.
  • [10] R. J. Fokkink, The structure of trajectories, Ph.D. thesis, Delft, 1992.
  • [11] L. Kailhofer, A partial classification of inverse limit spaces of tent maps with periodic critical points, Ph.D. thesis, Milwaukee, 1999.
  • [12] B. Mossé, Puissances de mots et reconnaissabilité des points fixes d'une substitution, Theoret. Comput. Sci.99 (1992), 327-334.
  • [13] S. Nadler, Continuum Theory, Marcel Dekker, New York, 1992.
  • [14] M. Queffélec, Substitution Dynamical Systems. Spectral Analysis, Lecture Notes in Math.1294, Springer, 1987.
  • [15] R. Swanson and H. Volkmer, Invariants of weak equivalence in primitive matrices, Ergodic Theory Dynam. Systems 20 (2000), 611-616.
  • [16] W. Watkins, Homeomorphic classification of certain inverse limit spaces with open bonding maps, Pacific J. Math.103 (1982), 589-601.
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bwmeta1.element.bwnjournal-article-fmv165i2p125bwm
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