Realization of tangent perturbations in discrete and continuous time conservative systems

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.

18 page

References in corpus (1)

• New solutions of the Jacobi equations for three-dimensional Poisson structures

Cited by in corpus (3)

• Conservative Replicator and Lotka-Volterra Equations in the context of Dirac$\backslash$ big-isotropic Structures
• Local perturbations of conservative $C^1$-diffeomorphisms
• Billiards in generic convex bodies have positive topological entropy