Lie symmetries of birational maps preserving genus 0 fibrations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Llorens, Mireia¹  Manosa, Victor² 

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

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

关键词: Integrable maps;    Lie symmetries;    Periodic orbits;    Rational parameterizations;   

DOI  :  10.1016/j.jmaa.2015.06.069

来源: Elsevier

【 摘 要 】

We prove that any planar birational integrable map, which preserves a fibration given by genus 0 curves has a Lie symmetry and some associated invariant measures. The obtained results allow to study in a systematic way the global dynamics of these maps. Using this approach, the dynamics of several maps is described. In particular we are able to give, for particular examples, the explicit expression of the rotation number function, and the set of periods of the considered maps. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free