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dc.contributor | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
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dc.contributor | Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
dc.contributor.author | Cima Mollet, Anna |
dc.contributor.author | Gasull Embid, Armengol |
dc.contributor.author | Mañosa Fernández, Víctor |
dc.date | 2013-11 |
dc.identifier.citation | Cima, A.; Gasull, A.; Mañosa, V. Global periodicity conditions for maps and recurrences via normal forms. "International journal of bifurcation and chaos", Novembre 2013, vol. 23, núm. 11, p. 1350182-1-1350182-18. |
dc.identifier.citation | 0218-1274 |
dc.identifier.citation | 10.1142/S0218127413501824 |
dc.identifier.uri | http://hdl.handle.net/2117/21188 |
dc.description.abstract | We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of K, 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. |
dc.description.abstract | Peer Reviewed |
dc.language.iso | eng |
dc.relation | http://www.worldscientific.com/doi/abs/10.1142/S0218127413501824 |
dc.rights | info:eu-repo/semantics/openAccess |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
dc.subject | Differential equations |
dc.subject | Differentiable dynamical systems |
dc.subject | Periodic orbits |
dc.subject | Normal forms |
dc.subject | Maps |
dc.subject | Difference Equations |
dc.subject | Equacions diferencials |
dc.subject | Sistemes dinàmics diferenciables |
dc.subject | Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory |
dc.subject | Classificació AMS::39 Difference and functional equations::39A Difference equations |
dc.subject | Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
dc.title | Global periodicity conditions for maps and recurrences via normal forms |
dc.type | info:eu-repo/semantics/submittedVersion |
dc.type | info:eu-repo/semantics/article |