On the set of periods of sigma maps of degree 1
Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Ruette, Sylvie (Université Paris-Sud 11. Laboratoire de Mathématiques)

Date:	2015
Abstract:	We study the set of periods of degree 1 continuous maps from σ into itself, where σ denotes the space shaped like the letter σ (i. e. , a segment attached to a circle by one of its endpoints). Since the maps under consideration have degree 1, the rotation theory can be used. We show that, when the interior of the rotation interval contains an integer, then the set of periods (of periodic points of any rotation number) is the set of all integers except maybe 1 or 2. We exhibit degree 1 σ-maps f whose set of periods is a combination of the set of periods of a degree 1 circle map and the set of periods of a 3-star (that is, a space shaped like the letter Y ). Moreover, we study the set of periods forced by periodic orbits that do not intersect the circuit of σ; in particular, when there exists such a periodic orbit whose diameter, at lifting level, is at least 1, then there exist periodic points of all periods.
Grants:	Ministerio de Economía y Competitividad MTM2008-01486 Ministerio de Economía y Competitividad MTM2011-26995-C02-01
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Degree one ; Large orbits ; Rotation set ; Set of periods ; Sigma maps ; Star maps
Published in:	Discrete and continuous dynamical systems. Series A, Vol. 35 Núm. 10 (2015) , p. 4683-4734, ISSN 1553-5231

DOI: 10.3934/dcds.2015.35.4683

Postprint 45 p, 678.8 KB

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