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Title:
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Global periodicity conditions for maps and recurrences via Normal Forms
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Author:
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Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions |
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Abstract:
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We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms 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 |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
-Differential equations
-Differentiable dynamical systems
-Periodic maps
-Linearization
-Normal Forms
-Rational parametrizations
-Globally periodic recurrences
-Lyness recurrences
-Equacions diferencials
-Sistemes dinàmics diferenciables
-Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
-Classificació AMS::39 Difference and functional equations::39A Difference equations
-Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
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Rights:
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Document type:
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Article - Draft
Other |
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