PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 47 | 1 | 91-108
Tytuł artykułu

The Conley index and countable decompositions of invariant sets

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We define a new cohomological index of Conley type associated to any bi-infinite sequence of neighborhoods that satisfies a certain isolation condition. We use this index to study the chaotic dynamics on invariant sets which decompose as countable unions of pairwise disjoint (mod 0) compact pieces.
Słowa kluczowe
Rocznik
Tom
47
Numer
1
Strony
91-108
Opis fizyczny
Daty
wydano
1999
Twórcy
autor
  • Department of Mathematical and Computer Sciences, Loyola University of Chicago, 6525 North Sheridan Road, Chicago, Illinois 60626, U.S.A.
Bibliografia
  • [1] L. A. Bunimovich, A Theorem on Ergodicity of Two-Dimensional Hyperbolic Billiards, Comm. Math. Phys. 130 (1990), 599-621.
  • [2] L. A. Bunimovich and Ya. G. Sinai, Markov Partitions for Dispersed Billiards, Comm. Math. Phys. 78 (1980), 247-280.
  • [3] M. Carbinatto, J. Kwapisz and K. Mischaikow, Horseshoes and the Conley Index Spectrum, preprint, CDSNS96-247.
  • [4] J. Degiovanni and M. Mrozek, The Conley Index for Maps in the Absence of Compactness, Proc. Royal Soc. Edinburgh 123A (1993), 79-95.
  • [5] M. Gidea, The Discrete Conley Index for Non-Invariant Sets, Proceedings of the Topological Methods in Differential Equations and Dynamical Systems Conference, Kraków, Poland, July (1996), to appear.
  • [6] M. Gidea, Leray Functor and Orbital Conley Index for Non-Invariant Sets, Discrete and Continuous Dynamical Systems, to appear.
  • [7] M. Gidea, The Discrete Conley Index for Non-Invariant Sets and Detection of Chaos, thesis (1997).
  • [8] A. Granas, The Leray-Schauder Index and the Fixed Point Index for Arbitrary ANR's, Bull. Soc. Math. France 100 (1972), 209-228.
  • [9] T. Kruger and S. Troubetzkoy, Markov Partitions and Shadowing for Non-Uniformly Hyperbolic Systems with Singularities, Erg. Th. Dyn. Sys. (1992), 487-508.
  • [10] K. Mischaikow, Conley Index Theory: Some recent development, preprint, CDSNS 94-181.
  • [11] K. Mischaikow and M. Mrozek, Chaos in Lorentz equation: A computer assisted proof, Bull. Amer. Math. Soc. 32 (1995), 66-72.
  • [12] K. Mischaikow and M. Mrozek, Isolating Neighborhoods and Chaos, Japan J. Indus. Appl. Math. 12 (1995), 205-236.
  • [13] M. Mrozek, Leray functor and the cohomological Conley index for discrete dynamical systems, Trans. Amer. Math. Soc. 318 (1990), 149-178.
  • [14] M. Mrozek, Index pairs and the fixed point index for semidynamical systems with discrete time, Fundamenta Mathematicae 133 (1989), 179-194.
  • [15] R. Srzednicki, A generalization of Lefschetz fixed point theorem and detection of chaos, preprint.
  • [16] E. H. Spanier, Algebraic Topology, McGraw-Hill, 1966.
  • [17] A. Szymczak, The Conley index for decompositions of isolated invariant sets, Fundamenta Mathematicae 148 (1995), 71-90.
  • [18] A. Szymczak, The Conley index for discrete semidynamical systems, Topology Appl., to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv47i1p91bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.