Global periodicity conditions for maps and recurrences via Normal Forms
Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)

Date:	2013
Abstract:	We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of Kk, where K is R or C, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437
Note:	Agraïments: The third author is supported by the grant DPI2011-25822
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Periodic maps ; Linearization ; Normal Forms ; Rational parametrizations ; Globally periodic recurrences ; Lyness recurrences
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 23 Núm. 11 (2013) , p. 1350182 (18 pages), ISSN 1793-6551

DOI: 10.1142/S0218127413501824

Postprint 25 p, 387.2 KB

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