Meromorphic first integrals of analytic diffeomorphisms
Ferragut Amengual, Antoni Manel (Universidad Internacional de La Rioja)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences)

Date:	2023
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.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agencia Estatal de Investigación CEX2020-001084-M Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Discrete dynamical system ; Integrability ; Meromorphic first integrals
Published in:	Journal of mathematical analysis and applications, Vol. 519, Issue 1 (March 2023) , art. 126796, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2022.126796

Available from: 2025-03-31 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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