Articulo Revista Indexada
Meromorphic first integrals of analytic diffeomorphisms
Registro en:
Ferragut, A., Gasull, A., & Zhang, X. (2023). Meromorphic first integrals of analytic diffeomorphisms. Journal of Mathematical Analysis and Applications, 519(1), 126796.
0022-247X
Autor
Ferragut, Antoni
Gasull, Armengol
Zhang, Xiang
Institución
Resumen
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.