Persistent homoclinic tangencies for conservative maps near the identity

Abstract

For families of conservative maps near the identity we prove the existence of open sets of parameters with persistence of homoclinic tangencies between stable and unstable leaves of ‘thick’ horse-shoes. Such families are obtained, for instance, by perturbing integrable Hamiltonian systems in $\mathbb{R}^2$ with a rapidly periodic oscillatory term and then performing a slowing change in the time variable.