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arXiv · 1310.1063

Realization of tangent perturbations in discrete and continuous time conservative systems

Hassan Najafi Alishah·João Lopes Dias
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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 $C^1$-close Poisson diffeomorphism. We also show that a similar property holds for the Poincaré 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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Hassan Najafi Alishah, João Lopes Dias. 2013-10-03. Realization of tangent perturbations in discrete and continuous time conservative systems. https://doi.org/10.3934/dcds.2014.34.5359

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