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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