Work

Coupling symmetries with Poisson structures

Year: 2013

Type: report

Abstract: We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's splitting theorem for the integrable system is also studied giving some examples in which such a splitting does not exist, i.e. when the integrable system is not, locally, a product of an integrable system on the symplectic leaf and an integrable system on a transversal. The problem of splitting for integrable systems with additional symmetries is also considered.

Source: RECERCAT (Consorci de Serveis Universitaris de Catalunya)

DOI: 10.48550/arxiv.1301.1329

Authors: Laurent-Gengoux, Camille, Miranda, Eva

Institution: Universitat Politècnica de Catalunya

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2949949163

Cites: 9

Cited by:

Related to: 20