Integrable deformations of Rossler and Lorenz systems from Poisson-Lie groups

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Ballesteros, Angel¹  Blasco, Alfonso¹  Musso, Fabio^1,2 

[1] Univ Burgos, Dept Fis, Burgos 09001, Spain

[2] IC Leonardo da Vinci, Via Grande Muraglia 37, I-0014 Rome, Italy

关键词: Integrability;    Deformations;    Coupled differential equations;    Rossler system;    Lorenz system;    Poisson-Lie groups;   

DOI  :  10.1016/j.jde.2016.02.014

来源: Elsevier

【 摘 要 】

A method to construct integrable deformations of Hamiltonian systems of ODEs endowed with Lie-Poisson symmetries is proposed by considering Poisson-Lie groups as deformations of Lie-Poisson (co)algebras. Moreover, the underlying Lie-Poisson symmetry of the initial system of ODEs is used to construct integrable coupled systems, whose integrable deformations can be obtained through the construction of the appropriate Poisson-Lie groups that deform the initial symmetry. The approach is applied in order to construct integrable deformations of both uncoupled and coupled versions of certain integrable types of Rossler and Lorenz systems. It is worth stressing that such deformations are of non-polynomial type since they are obtained through an exponentiation process that gives rise to the Poisson-Lie group from its infinitesimal Lie bialgebra structure. The full deformation procedure is essentially algorithmic and can be computerized to a large extent. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free