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Non-integrability of measure preserving maps via Lie symmetries
Cima, Anna
Gasull, Armengol
Mañosa, Víctor

Data: 2015
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Matèria: Cohen map ; difference equations ; Integrability and non-integrability of maps ; integrable vector fields ; Isochronous center ; Lie symmetries ; measure preserving maps ; Period function
Publicat a: Journal of Differential Equations, Vol. 259 (2015) , p. 5115-5136

DOI: 10.1016/j.jde.2015.06.019

25 p, 527.3 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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