Periods of periodic points of maps of the circle which have a fixed point-Reference-Cited by-同舟云学术

Periods of periodic points of maps of the circle which have a fixed point

Published:1981 Issue:3 Volume:82 Page:481-486
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Block Louis

Abstract

For a continuous map f f of the circle to itself, let P ( f ) P(f) denote the set of positive integers n n such that f f has a periodic point of (least) period n n . Results are obtained which specify those sets, which occur as P ( f ) P(f) , for some continuous map f f of the circle to itself having a fixed point. These results extend a theorem of Šarkovskii on maps of the interval to maps of the circle which have a fixed point.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1981-082-03/S0002-9939-1981-0612745-7/S0002-9939-1981-0612745-7.pdf

Reference4 articles.

1. Periodic orbits of continuous mappings of the circle;Block, Louis;Trans. Amer. Math. Soc.,1980

2. Periodic points and topological entropy of one-dimensional maps;Block, Louis,1980

3. Co-existence of cycles of a continuous mapping of the line into itself;Šarkovs′kiĭ, O. M.;Ukrain. Mat. \v{Z}.,1964

4. A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real line;Štefan, P.;Comm. Math. Phys.,1977

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