# Homeomorphisms of inverse limit spaces of one-dimensional maps

Fundamenta Mathematicae (1995)

- Volume: 146, Issue: 2, page 171-187
- ISSN: 0016-2736

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topBarge, Marcy, and Diamond, Beverly. "Homeomorphisms of inverse limit spaces of one-dimensional maps." Fundamenta Mathematicae 146.2 (1995): 171-187. <http://eudml.org/doc/212060>.

@article{Barge1995,

abstract = {We present a new technique for showing that inverse limit spaces of certain one-dimensional Markov maps are not homeomorphic. In particular, the inverse limit spaces for the three maps from the tent family having periodic kneading sequence of length five are not homeomorphic.},

author = {Barge, Marcy, Diamond, Beverly},

journal = {Fundamenta Mathematicae},

keywords = {inverse limit; one-dimensional Markov maps; periodic kneading sequence},

language = {eng},

number = {2},

pages = {171-187},

title = {Homeomorphisms of inverse limit spaces of one-dimensional maps},

url = {http://eudml.org/doc/212060},

volume = {146},

year = {1995},

}

TY - JOUR

AU - Barge, Marcy

AU - Diamond, Beverly

TI - Homeomorphisms of inverse limit spaces of one-dimensional maps

JO - Fundamenta Mathematicae

PY - 1995

VL - 146

IS - 2

SP - 171

EP - 187

AB - We present a new technique for showing that inverse limit spaces of certain one-dimensional Markov maps are not homeomorphic. In particular, the inverse limit spaces for the three maps from the tent family having periodic kneading sequence of length five are not homeomorphic.

LA - eng

KW - inverse limit; one-dimensional Markov maps; periodic kneading sequence

UR - http://eudml.org/doc/212060

ER -

## References

top- [1] J. M. Aarts and R. J. Fokkink, The classification of solenoids, Proc. Amer. Math. Soc. 111 (1991), 1161-1163. Zbl0768.54026
- [2] M. Barge, Horseshoe maps and inverse limits, Pacific J. Math. 121 (1986), 29-39. Zbl0601.58049
- [3] M. Barge and S. Holte, Nearly one-dimensional Henon attractors and inverse limits, preprint.
- [4] M. Barge and J. Martin, Chaos, periodicity and snake-like continua, Trans. Amer. Math. Soc. 289 (1985), 355-365. Zbl0559.58014
- [5] R. H. Bing, A simple closed curve is the only homogeneous bounded plane continuum that contains an arc, Canad. J. Math. 12 (1960), 209-230. Zbl0091.36204
- [6] P. Collet and J. P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston, 1980. Zbl0458.58002
- [7] W. Dębski, On topological types of the simplest indecomposable continua, Colloq. Math. 49 (1985), 203-211. Zbl0591.54026
- [8] F. R. Gantmacher, The Theory of Matrices, Vol. II, Chelsea, New York, 1959. Zbl0085.01001
- [9] J. Guckenheimer, Sensitive dependence to initial conditions for one-dimensional maps, Comm. Math. Phys. 70 (1979), 133-160. Zbl0429.58012
- [10] S. Holte, Generalized horseshoe maps and inverse limits, Pacific J. Math. 156 (1992), 297-305. Zbl0723.58034
- [11] S. Holte, Inverse limits of Markov interval maps, preprint. Zbl1010.37020
- [12] S. Holte and R. Roe, Inverse limits associated with the forced van der Pol equation, preprint. Zbl0813.58035
- [13] D. A. Lind, The entropies of topological Markov shifts and a related class of algebraic integers, Ergodic Theory Dynamical Systems 4 (1984), 283-300. Zbl0546.58035
- [14] M. C. McCord, Inverse limit sequences with covering maps, Trans. Amer. Math. Soc. 114 (1965), 197-209. Zbl0136.43603
- [15] J. Mioduszewski, Mappings of inverse limits, Colloq. Math. 10 (1963), 39-44. Zbl0118.18205
- [16] C. Robinson, Introduction to the Theory of Dynamical Systems, manuscript, July 1993.
- [17] B. L. van der Waerden, Modern Algebra, Ungar, New York, 1953.
- [18] W. T. Watkins, Homeomorphic classification of certain inverse limit spaces with open bonding maps, Pacific J. Math. 103 (1982), 589-601. Zbl0451.54027
- [19] R. Williams, One-dimensional nonwandering sets, Topology 6 (1967), 473-487. Zbl0159.53702

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