Different approaches to the global periodicity problem

Anna Cimà, Armengol Gasull, Víctor Mañosa Fernández, Francesc Mañosas Capellades

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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.
Idioma originalEnglish
Títol de la publicacióDifference Equations, Discrete Dynamical Systems and Applications
Lloc de publicacióCham, Switzerland:
EditorSpringer, Cham
Nombre de pàgines22
ISBN (electrònic)978-3-662-52927-0
Estat de la publicacióAcceptat en premsa - 2016


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