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1994-1995 | 146 | 2 | 171-187
Tytuł artykułu

Homeomorphisms of inverse limit spaces of one-dimensional maps

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
146
Numer
2
Strony
171-187
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-11-03
poprawiono
1994-05-08
Twórcy
autor
  • Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717, U.S.A., barge@math.montana.edu
  • Department of Mathematics, University of Charleston, Charleston, South Carolina 29424, U.S.A., diamondb@cofc.edu
Bibliografia
  • [1] J. M. Aarts and R. J. Fokkink, The classification of solenoids, Proc. Amer. Math. Soc. 111 (1991), 1161-1163.
  • [2] M. Barge, Horseshoe maps and inverse limits, Pacific J. Math. 121 (1986), 29-39.
  • [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.
  • [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.
  • [6] P. Collet and J. P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston, 1980.
  • [7] W. Dębski, On topological types of the simplest indecomposable continua, Colloq. Math. 49 (1985), 203-211.
  • [8] F. R. Gantmacher, The Theory of Matrices, Vol. II, Chelsea, New York, 1959.
  • [9] J. Guckenheimer, Sensitive dependence to initial conditions for one-dimensional maps, Comm. Math. Phys. 70 (1979), 133-160.
  • [10] S. Holte, Generalized horseshoe maps and inverse limits, Pacific J. Math. 156 (1992), 297-305.
  • [11] S. Holte, Inverse limits of Markov interval maps, preprint.
  • [12] S. Holte and R. Roe, Inverse limits associated with the forced van der Pol equation, preprint.
  • [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.
  • [14] M. C. McCord, Inverse limit sequences with covering maps, Trans. Amer. Math. Soc. 114 (1965), 197-209.
  • [15] J. Mioduszewski, Mappings of inverse limits, Colloq. Math. 10 (1963), 39-44.
  • [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.
  • [19] R. Williams, One-dimensional nonwandering sets, Topology 6 (1967), 473-487.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv146i2p171bwm
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