The splitting of separatrices of hyperbolic fixed points for exact symplectic maps of n degrees
of freedom is considered. The non-degenerate critical points of a real-valued function (called …

We study families of volume preserving diffeomorphisms in R 3 that have a pair of hyperbolic
fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to …

We study perturbations of diffeomorphisms that have a saddle connection between a pair of
normally hyperbolic invariant manifolds. We develop a first-order deformation calculus for …

We develop a Melnikov method for volume-preserving maps that have normally hyperbolic
invariant sets with codimension-one invariant manifolds. The Melnikov function is shown to …

The dynamical system arising from the problem of billiards is a classical example where the
theory of twist maps can be applied. In the case of an elliptic billiard table, the corresponding …

We construct a family of integrable volume-preserving maps in R^3 with a two-dimensional
heteroclinic connection of spherical shape between two fixed points of saddle-focus type. In …

Explicit formulae are given for the saddle connection of an integrable family of standard
maps studied by Y. Suris [Func. Anal. Appl. 23 (1989) 74–76]. When the map is perturbed …

We study in this article the topological entropy of billiard systems on a convex domain of the
Euclidean plane. We restrict our attention to those systems whose boundary curve has …

The dynamical system arising from the problem of billiards is a classical example where the
theory of twist maps can be applied. In the case of an elliptic billiard table, the corresponding …

In this paper, a simple criterion to prove non-integrability of symplectic, perturbed twist
mappings in 2n-dimensions is developed for sufficiently small perturbations. In addition, an …