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.
@article{bwmeta1.element.bwnjournal-article-fmv146i2p171bwm,
author = {Marcy Barge and Beverly Diamond},
title = {Homeomorphisms of inverse limit spaces of one-dimensional maps},
journal = {Fundamenta Mathematicae},
volume = {146},
year = {1995},
pages = {171-187},
zbl = {0851.54037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv146i2p171bwm}
}
Barge, Marcy; Diamond, Beverly. Homeomorphisms of inverse limit spaces of one-dimensional maps. Fundamenta Mathematicae, Tome 146 (1995) pp. 171-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv146i2p171bwm/
[00000] [1] J. M. Aarts and R. J. Fokkink, The classification of solenoids, Proc. Amer. Math. Soc. 111 (1991), 1161-1163. | Zbl 0768.54026
[00001] [2] M. Barge, Horseshoe maps and inverse limits, Pacific J. Math. 121 (1986), 29-39. | Zbl 0601.58049
[00002] [3] M. Barge and S. Holte, Nearly one-dimensional Henon attractors and inverse limits, preprint.
[00003] [4] M. Barge and J. Martin, Chaos, periodicity and snake-like continua, Trans. Amer. Math. Soc. 289 (1985), 355-365. | Zbl 0559.58014
[00004] [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. | Zbl 0091.36204
[00005] [6] P. Collet and J. P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston, 1980. | Zbl 0458.58002
[00006] [7] W. Dębski, On topological types of the simplest indecomposable continua, Colloq. Math. 49 (1985), 203-211. | Zbl 0591.54026
[00007] [8] F. R. Gantmacher, The Theory of Matrices, Vol. II, Chelsea, New York, 1959. | Zbl 0085.01001
[00008] [9] J. Guckenheimer, Sensitive dependence to initial conditions for one-dimensional maps, Comm. Math. Phys. 70 (1979), 133-160. | Zbl 0429.58012
[00009] [10] S. Holte, Generalized horseshoe maps and inverse limits, Pacific J. Math. 156 (1992), 297-305. | Zbl 0723.58034
[00010] [11] S. Holte, Inverse limits of Markov interval maps, preprint. | Zbl 1010.37020
[00011] [12] S. Holte and R. Roe, Inverse limits associated with the forced van der Pol equation, preprint. | Zbl 0813.58035
[00012] [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. | Zbl 0546.58035
[00013] [14] M. C. McCord, Inverse limit sequences with covering maps, Trans. Amer. Math. Soc. 114 (1965), 197-209. | Zbl 0136.43603
[00014] [15] J. Mioduszewski, Mappings of inverse limits, Colloq. Math. 10 (1963), 39-44. | Zbl 0118.18205
[00015] [16] C. Robinson, Introduction to the Theory of Dynamical Systems, manuscript, July 1993.
[00016] [17] B. L. van der Waerden, Modern Algebra, Ungar, New York, 1953.
[00017] [18] W. T. Watkins, Homeomorphic classification of certain inverse limit spaces with open bonding maps, Pacific J. Math. 103 (1982), 589-601. | Zbl 0451.54027
[00018] [19] R. Williams, One-dimensional nonwandering sets, Topology 6 (1967), 473-487. | Zbl 0159.53702