Inverse limit spaces of post-critically finite tent maps

Henk Bruin

Fundamenta Mathematicae (2000)

  • Volume: 165, Issue: 2, page 125-138
  • ISSN: 0016-2736

Abstract

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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].

How to cite

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Bruin, Henk. "Inverse limit spaces of post-critically finite tent maps." Fundamenta Mathematicae 165.2 (2000): 125-138. <http://eudml.org/doc/212462>.

@article{Bruin2000,
abstract = {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].},
author = {Bruin, Henk},
journal = {Fundamenta Mathematicae},
keywords = {inverse limit space; interval map; tent map},
language = {eng},
number = {2},
pages = {125-138},
title = {Inverse limit spaces of post-critically finite tent maps},
url = {http://eudml.org/doc/212462},
volume = {165},
year = {2000},
}

TY - JOUR
AU - Bruin, Henk
TI - Inverse limit spaces of post-critically finite tent maps
JO - Fundamenta Mathematicae
PY - 2000
VL - 165
IS - 2
SP - 125
EP - 138
AB - 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].
LA - eng
KW - inverse limit space; interval map; tent map
UR - http://eudml.org/doc/212462
ER -

References

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  1. [1] C. Bandt, Composants of the horseshoe, Fund. Math.144 (1994), 231-241. Zbl0818.54028
  2. [2] M. Barge and B. Diamond, Homeomorphisms of inverse limit spaces of one-dimensional maps, ibid.146 (1995), 171-187. 
  3. [3] M. Barge and S. Holte, Nearly one-dimensional Hénon attractors and inverse limits, Nonlinearity8 (1995), 29-42. 
  4. [4] M. Barge and W. Ingram, Inverse limits on [0,1] using logistic bonding maps, Topology Appl.72 (1996), 159-172. Zbl0859.54030
  5. [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. Zbl0826.58023
  6. [6] K. Brucks and B. Diamond, A symbolic representation of inverse limit spaces for a class of unimodal maps, ibid., 207-226. Zbl0828.58011
  7. [7] H. Bruin, Planar embeddings of inverse limit spaces of unimodal maps, Topology Applications96 (1999), 191-208. Zbl0954.54019
  8. [8] A. Douady et J. Hubbard, Étude dynamique des polynômes complexes, partie I, Publ. Math. Orsay 85-04, 1984. Zbl0552.30018
  9. [9] F. Durand, A generalization of Cobham's Theorem, Theory Comput. Syst.31 (1998), 169-185. Zbl0895.68081
  10. [10] R. J. Fokkink, The structure of trajectories, Ph.D. thesis, Delft, 1992. 
  11. [11] L. Kailhofer, A partial classification of inverse limit spaces of tent maps with periodic critical points, Ph.D. thesis, Milwaukee, 1999. Zbl1032.54021
  12. [12] B. Mossé, Puissances de mots et reconnaissabilité des points fixes d'une substitution, Theoret. Comput. Sci.99 (1992), 327-334. Zbl0763.68049
  13. [13] S. Nadler, Continuum Theory, Marcel Dekker, New York, 1992. 
  14. [14] M. Queffélec, Substitution Dynamical Systems. Spectral Analysis, Lecture Notes in Math.1294, Springer, 1987. 
  15. [15] R. Swanson and H. Volkmer, Invariants of weak equivalence in primitive matrices, Ergodic Theory Dynam. Systems 20 (2000), 611-616. Zbl0984.37019
  16. [16] W. Watkins, Homeomorphic classification of certain inverse limit spaces with open bonding maps, Pacific J. Math.103 (1982), 589-601. Zbl0451.54027

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