On strong chain recurrence for maps

• Autorzy: Katsuya Yokoi
• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with strong chain recurrence introduced by Easton. We investigate the depth of the transfinite sequence of nested, closed invariant sets obtained by iterating the process of taking strong chain recurrent points, which is a related form of the central sequence due to Birkhoff. We also note the existence of a Lyapunov function which is decreasing off the strong chain recurrent set. As an application, we give a necessary and sufficient condition for the coincidence of the strong chain recurrence set and the chain recurrence set. Several examples are given to illustrate the difference between the concepts of strong chain recurrence and chain recurrence.

Kategorie tematyczne

• 37B20: Notions of recurrence
• 37B25: Lyapunov functions and stability; attractors, repellers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 114
• Numer: 2
• Strony: 165-177

Daty

wydano

2015

Twórcy

autor

Katsuya Yokoi

• Department of Mathematics, Jikei University School of Medicine, Chofu, Tokyo 182-8570, Japan

Identyfikatory

DOI

10.4064/ap114-2-6