Meromorphic first integrals of analytic diffeomorphisms

被引：0

作者：

Ferragut, Antoni ^{[1
]}

Gasull, Armengol ^{[2
,3
]}

Zhang, Xiang ^{[4
,5
]}

机构：

[1] Univ Int La Rioja, Ave Paz 137, Logrono 26006, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain

[3] Ctr Recerca Matemat, Barcelona 08193, Spain

[4] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, Shanghai 200240, Peoples R China

[5] Shanghai Jiao Tong Univ, CAM Shanghai, Shanghai 200240, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 519卷 / 01期

关键词：

Discrete dynamical system; Integrability; Meromorphic first integrals; SYSTEMS; INTEGRABILITY;

D O I：

10.1016/j.jmaa.2022.126796

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Poincare 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. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：15

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