PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 47 | 1 | 67-78
Tytuł artykułu

Connection matrix theory for discrete dynamical systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In [C] and [F1] the connection matrix theory for Morse decomposition is developed in the case of continuous dynamical systems. Our purpose is to study the case of discrete time dynamical systems. The connection matrices are matrices between the homology indices of the sets in the Morse decomposition. They provide information about the structure of the Morse decomposition; in particular, they give an algebraic condition for the existence of connecting orbit set between different Morse sets.
Słowa kluczowe
Rocznik
Tom
47
Numer
1
Strony
67-78
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
  • [BD] P. Bartłomiejczyk and Z. Dzedzej, Index filtrations and Morse decompositions for discrete dynamical systems, submitted to Annales Polonici Math.
  • [C] C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conf. Ser. in Math. 38, AMS, Providence, R.I., 1980.
  • [CoZ] C. Conley and R. Zehnder, Morse-type index theory for flows and periodic solutions for Hamoltonian systems, Comm. Pure Appl. Math. 37 (1984), 207-253.
  • [D] A. Dold, Lectures on algebraic topology, Springer Verlag, Berlin Heidelberg New York 1972.
  • [F1] R. Franzosa, Index filtrations and connection matrices for partially ordered Morse decompositions, Trans. Amer. Math. Soc. 298 (1986), 193-213.
  • [F2] R. Franzosa, The connection matrix theory for Morse decompositions, Trans. Amer. Math. Soc. 311 (1989), 561-592.
  • [M1] M. Mrozek, Index pairs and the fixed point index for semidynamical systems with discrete time, Fund. Math. 133 (1989), 179-194.
  • [M2] M. Mrozek, Leray functor and cohomological Conley index for discrete dynamical systems, Trans. Amer. Math. Soc. 318 (1990), 149-178.
  • [M3] M. Mrozek, Morse equation in Conley's index theory for homeomorphisms, Topology Appl. 38 (1991), 45-60.
  • [R] D. Richeson, Connection matrix pairs for the discrete Conley index, to appear in Trans. Amer. Math. Soc.
  • [Sal] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc. 291 (1985), 1-41.
  • [Szy] A. Szymczak, The Conley index for discrete dynamical systems, Topology Appl. 66 (1995), 215-240.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv47i1p67bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.