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1999 | 160 | 3 | 219-246
Tytuł artykułu

Subcontinua of inverse limit spaces of unimodal maps

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as subcontinua.
Słowa kluczowe
Rocznik
Tom
160
Numer
3
Strony
219-246
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-03-11
poprawiono
1999-02-12
Twórcy
autor
  • Mathematical Sciences, University of Wisconsin-Milwaukee Milwaukee, WI 53201, U.S.A., kmbrucks@csd.uwm.edu
autor
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, K. Brucks and B. Diamond, Self-similarity in inverse limit spaces of the tent family, Proc. Amer. Math. Soc. 124 (1996), 3563-3570.
  • [4] M. Barge and B. Diamond, Homeomorphisms of inverse limit spaces of one-dimensional maps, Fund. Math. 146 (1995), 171-187.
  • [5] M. Barge and B. Diamond, Inverse limit spaces of infinitely renormalizable maps, Topology Appl. 83 (1998), 103-108.
  • [6] M. Barge and B. Diamond, Subcontinua of the closure of the unstable manifold at a homoclinic tangency, Ergodic Theory Dynam. Systems 19 (1999), 1-19.
  • [7] M. Barge and S. Holte, Nearly one-dimensional Hénon attractors and inverse limits, Nonlinearity 8 (1995), 29-42.
  • [8] M. Barge and J. Martin, Endpoints of inverse limit spaces and dynamics, in: Continua with the Houston Problem Book (Cincinnati, OH, 1994), Lecture Notes in Pure and Appl. Math. 170, Dekker, New York, 1995, 165-182.
  • [9] M. Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478-483.
  • [10] K. Brucks, B. Diamond, M. V. Otero-Espinar and C. Tresser, Dense orbits of critical points for the tent map, in: Contemp. Math. 117, Amer. Math. Soc., Providence, RI, 1991, 57-61.
  • [11] H. Bruin, Invariant measures of interval maps, Ph.D. thesis, Delft, 1994.
  • [12] H. Bruin, Combinatorics of the kneading map, Internat J. Bifur. and Chaos Appl. Sci. Engrg. 5 (1995), 1339-1349.
  • [13] H. Bruin, Planar embeddings of inverse limit spaces of unimodal maps, Topology Appl., to appear.
  • [14] H. Bruin, Inverse limit spaces of post-critically finite tent maps, preprint, 1998.
  • [15] D W. Dębski, On topological types of the simplest indecomposable continua, Colloq. Math. 49 (1985), 203-211.
  • [16] F. Hofbauer, The topological entropy of the transformation x ↦ ax(1-x), Monatsh. Math. 90 (1980), 117-141.
  • [17] F. Hofbauer and G. Keller, Quadratic maps without asymptotic measure, Comm. Math. Phys. 127 (1990), 319-337.
  • [18] S. Holte, Generalized horseshoe maps and inverse limits, Pacific J. Math. 156 (1992), 297-305.
  • [19] W. de Melo and S. van Strien, One-Dimensional Dynamics, Springer, New York, 1993.
  • [20] J. Mioduszewski, Mappings of inverse limits, Colloq. Math. 10 (1963), 39-44.
  • [21] S. Nadler, Continuum Theory, Dekker, New York, 1992.
  • [22] R. C. Swanson and H. W. Volkmer, Invariants of weak equivalence in primitive matrices, preprint, 1998.
  • [23] W W. T. Watkins, Homeomorphic classification of certain inverse limit spaces with open bonding maps, Pacific J. Math. 103 (1982), 589-601.
  • [24] R. F. Williams, One-dimensional nonwandering sets, Topology 6 (1967), 473-487.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv160i3p219bwm
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