2013/08/01 by R. Flores-Espinoza, Ruben Flores-Espinoza, Flores-Espinoza, Ruben
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1308.0307
arxiv created 2013/08/01 · openalex publication_date 2013/08/01 · arxiv updated 2013/08/02 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
By means of the Schouten calculus for contravariant antisymmetric tensor fields, we apply the Lie transform method to investigate smooth deformations of tensor fields and, in particular, to perturbations of Hamiltonian systems generated by deformations of the Poisson bracket. Using results by Karasev and Vorobiev on the computation of Poisson cohomology we describe infinitesimal generators for the Lie transformations. We give applications to perturbed Euler equations on six dimensional Lie coalgebras and to Hamiltonian systems on Poisson manifolds equipped with Dirac brackets.