On a Morse decomposition of an isolated invariant set of a homeomorphism (discrete dynamical system) there are partial orderings defined by the homeomorphism. These are called admissible orderings of the Morse decomposition. We prove the existence of index filtrations for admissible total orderings of a Morse decomposition and introduce the connection matrix in this case.
Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
[C] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Regional Conf. Ser. in Math. 38, Amer. Math. Soc., Providence, 1980.
[CoZ] C. Conley and R. Zehnder, Morse-type index theory for flows and periodic solutions for Hamiltonian systems, Comm. Pure Appl. Math. 37 (1984), 207-253.
[Fra1] R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. Amer. Math. Soc. 298 (1986), 193-213.
[Fra2] R. Franzosa, The connection matrix theory for Morse decompositions, ibid. 311 (1989), 561-592.
[Mr1] M. Mrozek, Index pairs and the fixed point index for semidynamical systems with discrete time, Fund. Math. 133 (1989), 179-194.
[Mr2] M. Mrozek, Leray functor and cohomological Conley index for discrete dynamical systems, Trans. Amer. Math. Soc. 318 (1990), 149-178.
[Mr3] M. Mrozek, Morse equation in Conley's index theory for homeomorphisms, Topology Appl. 38 (1991), 45-60.
[Re] J. Reineck, The connection matrix in Morse-Smale flows II, Trans. Amer. Math. Soc. 347 (1995), 2097-2110.
[Ri] D. Richeson, Connection matrix pairs for the discrete Conley index, ibid., to appear.
[Sal] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, ibid. 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-apmv72z1p51bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.