The period adding and incrementing bifurcations: from rotation theory to applications
Granados, Albert (Technical University of Denmark. Department of Applied Mathematics and Computer Science)
Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Krupa, Maciej (Inria Sophia-Antipolis Research Center (França))

Date:	2017
Abstract:	This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through this literature to prove sufficient conditions for the occurrence of two types of bifurcation scenarios involving rich dynamics. The first scenario consists of the appearance of periodic orbits whose symbolic sequences and "rotation" numbers follow a Farey tree structure; the periods of the periodic orbits are given by consecutive addition. This is called the period adding bifurcation, and its proof relies on results for maps on the circle. In the second scenario, symbolic sequences are obtained by consecutive attachment of a given symbolic block and the periods of periodic orbits are incremented by a constant term. It is called the period incrementing bifurcation, in its proof relies on results for maps on the interval.
Grants:	Ministerio de Economía y Competitividad MTM2012-31714 Ministerio de Economía y Competitividad MTM2011-26995-C02-01
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Devil's staircase ; Discontinuous circle maps ; Farey Tree ; Period adding ; Period incrementing ; Piecewise-smooth maps
Published in:	SIAM Review, Vol. 59 Núm. 2 (2017) , p. 225-292, ISBN 0036-1445 (print)

DOI: 10.1137/140996598

Postprint 83 p, 5.0 MB

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