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00925njm 22002777a 4500 dc Cima Mollet, Anna author Gasull Embid, Armengol author Mañosa Fernández, Víctor author 2015-11-15 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. Peer Reviewed Postprint (author’s final draft) 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::37C Smooth dynamical systems: general theory Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::39 Difference and functional equations::39A Difference equations Non-integrability of measure preserving maps via Lie symmetries