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Abstract
Let F be a real or complex ndimensional 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 mdimensional 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.
Original language  English 

Title of host publication  Difference Equations, Discrete Dynamical Systems and Applications 
Place of Publication  Cham, Switzerland: 
Publisher  Springer, Cham 
Pages  0085106 
Number of pages  22 
Volume  180 
Edition  2016 
ISBN (Electronic)  9783662529270 
DOIs  
Publication status  Accepted in press  2016 
Keywords
 Globally periodic maps
 Integrable discrete systems
 Lie Symmetries
 Linearizations
 Periodic difference equations
 Reversible maps
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 1 Active

Sistemas dinámicos contínuos y discretos: bifurcaciones, orbitas periódicas, integrabilidad y aplicaciones
Torregrosa i Arús, J. (Principal Investigator), Garrido Pelaez, J. M. (Collaborator), Jimenez Ruiz, J. J. (Collaborator), Mañosas Capellades, F. (Collaborator), Artes Ferragud, J. C. (Investigator), Cima Mollet, A. M. (Investigator), Corbera Subirana, M. (Investigator), Cors Iglesias, J. M. (Investigator), Gasull Embid, A. (Investigator), Mañosa Fernández, V. (Investigator), Pantazi, C. (Investigator) & Mayayo Cortasa, T. (Collaborator)
1/09/23 → 31/08/26
Project: Research Projects and Other Grants