Homoclinic and non-wandering points for maps of the circle-Reference-Cited by-同舟云学术

Homoclinic and non-wandering points for maps of the circle

Published:1983-12 Issue:4 Volume:3 Page:521-532
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

Block Louis,Coven Ethan,Mulvey Irene,Nitecki Zbigniew

Abstract

AbstractFor continuous maps ƒ of the circle to itself, we show: (A) the set of nonwandering points of ƒ coincides with that of ƒn for every odd n; (B) ƒ has a horseshoe if and only if it has a non-wandering homoclinic point; (C) if the set of periodic points is closed and non-empty, then every non-wandering point is periodic.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference12 articles.

1. Horseshoes for mappings of the interval;Misiurewicz;Bull. Acad. Polon. Sci. Ser. Sci. Math.,1979

2. Homoclinic points of mappings of the interval

3. Minimizing topological entropy for maps of the circle

4. Non-wandering sets of the powers of maps of the interval

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