Meromorphic first integrals of analytic diffeomorphisms
Dynamical Systems
2020-12-07 v1
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 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 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.
Cite
@article{arxiv.2012.02514,
title = {Meromorphic first integrals of analytic diffeomorphisms},
author = {Antoni Ferragut and Armengol Gasull and Xiang Zhang},
journal= {arXiv preprint arXiv:2012.02514},
year = {2020}
}