English

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 C1C^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.

Keywords

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}
}

Comments

18 page