%0 Journal Article
%T Realization of tangent perturbations in discrete and continuous time conservative systems
%A Hassan Najafi Alishah
%A Jo£żo Lopes Dias
%J Mathematics
%D 2013
%I arXiv
%R 10.3934/dcds.2014.34.5359
%X 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 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.
%U http://arxiv.org/abs/1310.1063v1