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Title:
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Non-integrability of measure preserving maps via Lie symmetries
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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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Preprint. |
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Abstract:
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We consider the problem of characterizing, for certain natural
number m, the local C^m-non-integrability near
elliptic fixed points of smooth planar measure preserving maps. Our
criterion relates this non-integrability with the existence of some
Lie Symmetries associated to the maps, together with the study of
the finiteness of its periodic points. One of the steps in the proof
uses the regularity of the period function on the whole period
annulus for non-degenerate centers, question that we believe that is
interesting by itself. The obtained criterion can be applied to
prove the local non-integrability of the Cohen map and of several
rational maps coming from second order difference equations. |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
-Differentiable dynamical systems
-Differential equations
-Integrability and non-integrability of
maps
-Measure preserving maps
-Lie symmetries
-Integrable vector
fields
-Period function
-Isochronous centers
-Cohen map
-Difference
equations.
-Sistemes dinàmics diferenciables
-Equacions diferencials ordinàries
-Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
-Classificació AMS::37 Dynamical systems and ergodic theory
-Classificació AMS::39 Difference and functional equations::39A Difference equations |
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Rights:
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Document type:
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Article - Draft
Report |
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