Meromorphic first integrals of analytic diffeomorphisms

Antoni Ferragut; Armengol Gasull; Xiang Zhang

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Meromorphic first integrals of analytic diffeomorphisms

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arxiv 2012.02514 v1 pith:2WT4LIHJ submitted 2020-12-04 math.DS

Meromorphic first integrals of analytic diffeomorphisms

Antoni Ferragut , Armengol Gasull , Xiang Zhang This is my paper

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We give an upper bound for the number of functionally independent meromorphic first integrals that a discrete dynamical system generated by an analytic map $f$ can have in a neighborhood of one of its fixed points. This bound is obtained in terms of the resonances among the eigenvalues of the differential of $f$ at this point. Our approach is inspired on similar Poincar\'e type results for ordinary differential equations. We also apply our results to several examples, some of them motivated by the study of several difference equations.

Meromorphic first integrals of analytic diffeomorphisms

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