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.
CitationCima, A.; Gasull, A.; Mañosa, V. "Non-integrability of measure preserving maps via Lie symmetries". 2015.
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