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Global periodicity conditions for maps and recurrences via Normal Forms
Cima, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data: 2013
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Linearization ; Periodic maps; 653 1_ ; Normal Forms ; Rational parametrizations ; Globally periodic recurrences ; Lyness recurrences
Publicat a: 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

25 p, 387.2 KB

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