Local perturbations of conservative $C^1$-diffeomorphisms

Abstract

A number of techniques have been developed to perturb the dynamics of $C^1$-diffeomorphisms and to modify the properties of their periodic orbits. For instance, one can locally linearize the dynamics, change the tangent dynamics, or create local homoclinic orbits. These techniques have been crucial for the understanding of $C^1$ dynamics, but their most precise forms have mostly been shown in the dissipative setting. This work extends these results to volume-preserving and especially symplectic systems. These tools underlie our study of the entropy of $C^1$-diffeomorphisms in (arxiv:1606.01765). We also give an application to the approximation of transitive invariant sets without genericity assumptions.

31 pages, companion to the paper Entropy of C1 diffeomorphisms without a dominated splitting (arxiv:1606.01765)

References in corpus (1)

• Realization of tangent perturbations in discrete and continuous time conservative systems

Cited by in corpus (1)

• Billiards in generic convex bodies have positive topological entropy