Meromorphic first integrals of analytic diffeomorphisms

Abstract

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 Poincaré 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.

References in corpus (5)

• Analytic integrable systems: Analytic normalization and embedding flows
• Generalized rational first integrals of analytic differential systems
• Studying discrete dynamical systems trough differential equations
• Some properties of the k-dimensional Lyness' map
• Integrability and non-integrability of periodic non-autonomous Lyness recurrences