Studying discrete dynamical systems through differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:244

Article

Cima, Anna²  Gasull, Armengol²  Manosa, Victor¹ 

[1] Univ Politecn Cataluna, Control Dynam & Applicat Grp CoDALab, Dept Matemat Aplicada 3, Terrassa 08222, Spain

[2] Univ Autonoma Barcelona, Fac Ciencies, Dept Matemat, E-08193 Barcelona, Spain

关键词: conjugation of flows;    lie symmetries;    integrable vector fields;    integrable mappings;    difference equations;   

DOI  :  10.1016/j.jde.2007.10.013

来源: Elsevier

【 摘 要 】

In this paper we consider dynamical systems generated by a diffeonnorphism F defined on U an open subset of R-n, and give conditions over F which imply that their dynamics can be understood by studying the flow of an associated differential equation, <(x)over dot> = X (x), also defined on U. In particular the case where F has n - 1 functionally independent first integrals is considered. In this case X is constructed by imposing that it shares with F the same set of first integrals and that the functional equation mu(F(x)) = det(DF(x))mu(x), X epsilon u, has some non-zero solution, mu. Several examples for n = 2, 3 are presented, most of them coming from several well-known difference equations. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free