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Pàgina inicial > Llibres i col·leccions > Capítols de llibres > Different approaches to the global periodicity problem |
Publicació: | Cham, Switzerland: Springer, 2016 |
Descripció: | 21 pàg. |
Resum: | Let F be a real or complex n-dimensional map. It is said that F is globally periodic if there exists some p ∈ ℕ such that F(x) = x for all x, where F = F ◦ F , k ≥ 2. The minimal p satisfying this property is called the period of F. Given a m-dimensional parametric family of maps, say F, a problem of current interest is to determine all the values of λ such that F is globally periodic, together with their corresponding periods. The aim of this paper is to show some techniques that we use to face this question, as well as some recent results that we have obtained. We will focus on proving the equivalence of the problem with the complete integrability of the dynamical system induced by the map F, and related issues; on the use of the local linearization given by the Bochner Theorem; and on the use the Normal Form theory. We also present some open questions in this setting. |
Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad DPI2011-25822 Ministerio de Economía y Competitividad DPI2016-77407-P Ministerio de Economía y Competitividad MTM2011-26995-C02-01 |
Nota: | Publicació amb motiu de la International Conference on Difference Equations and Applications (July 22-27, 2012, Barcelona, Spain) amb el títol Difference Equations, Discrete Dynamical Systems and Applications |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Col·lecció: | Springer Proceedings in Mathematics & Statistics ; 180 |
Document: | Capítol de llibre ; recerca ; Versió acceptada per publicar |
Matèria: | Globally periodic maps ; Integrable discrete systems ; Lie Symmetries ; Linearizations ; Periodic difference equations ; Reversible maps |
Publicat a: | Difference Equations, Discrete Dynamical Systems and Applications, 2016, p. 85-106, ISBN 978-3-662-52927-0 |
Postprint 21 p, 185.3 KB |