Periodic Orbits and the Continuity of Rotation Numbers

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1993Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 117, page 269 (issn: 0002-9939,

Copyright policy )

Authors: Swanson, Richard;

doi: 10.2307/2159726 , 10.1090/s0002-9939-1993-1112502-x

Periodic Orbits and the Continuity of Rotation Numbers

- Summary
- Subjects
- Metrics

Abstract

The main result is that an annulus homeomorphism homotopic to the identity either has a well-defined and continuous assignment of rotation numbers on its chain recurrent set or there exists an interval of rotation numbers and periodic points corresponding to each reduced rational number in the interval. As a corollary, rotational discontinuities force the mapping to admit periodic points of all sufficiently large periods n n . In a related result, we provide a criterion for the rotation set of an annulus homeomorphism to be nowhere dense.

Keywords

Local and nonlocal bifurcation theory for dynamical systems, chain recurrent set, rotation number, periodic orbits

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	5
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average