Non-integrability of measure preserving maps via Lie symmetries
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:	2015
Abstract:	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.
Grants:	Ministerio de Economía y Competitividad MTM2013-40998-P Ministerio de Economía y Competitividad DPI2011-25822 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-859 European Commission 318999
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Cohen map ; Difference equations ; Integrability and non-integrability of maps ; Integrable vector fields ; Isochronous center ; Lie symmetries ; Measure preserving maps ; Period function
Published in:	Journal of differential equations, Vol. 259 (2015) , p. 5115-5136, ISSN 1090-2732

DOI: 10.1016/j.jde.2015.06.019

Postprint 25 p, 527.3 KB

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