Topological approach to chain recurrence in continuous dynamical systems

• Autorzy: Oprocha P.
• Języki publikacji: EN

Abstrakty

EN

In this paper we present equivalent definitions of chain recurrent set for continuous dynamical systems. This definition allow us to define chain recurrent set in topological spaces.

Słowa kluczowe

EN

chain-recurrent set; continuous dynamical system; flow; attractor

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2005
• Tom: Vol. 25, no. 2
• Strony: 261--268
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Oprocha P.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland; and Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland,

Bibliografia

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• [3] Block L. S., Coppel W. A.: Dynamics in One Dimension. Lec. Notes in Math., Springer-Verlag 1992
• [4] Conley C.C.: The gradient structure of the flow: I. Ergodic Th. Dynam. Systems 8 (1988) 11-26
• [5] Franke J.E., Selgrade J.F.: Abstract u;-limit set, chain-recurrent sets and basic sets for flows. Proc. Amer. Math. Soc. 60 (1976) 309-316
• [6] Franke J.E., Selgrade J.F.: Hyperbolicity and Chain Recurence. J. Diff. Eq. 26 (1977) 27-36
• [7] Kuratowski: Topology. Vol II, Academic Press and Polish Scientific Publishers 1968