Realization of tangent perturbations in discrete and continuous time conservative systems
Dynamical Systems
2014-07-09 v1 Symplectic Geometry
Abstract
We prove that any perturbation of the symplectic part of the derivative of a Poisson diffeomorphism can be realized as the derivative of a -close Poisson diffeomorphism. We also show that a similar property holds for the Poincar\'e map of a Hamiltonian on a Poisson manifold. These results are the conservative counterparts of the Franks lemma, a perturbation tool used in several contexts most notably in the theory of smooth dynamical systems.
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Cite
@article{arxiv.1310.1063,
title = {Realization of tangent perturbations in discrete and continuous time conservative systems},
author = {Hassan Najafi Alishah and João Lopes Dias},
journal= {arXiv preprint arXiv:1310.1063},
year = {2014}
}
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18 page