This is a survey of the main results related to separatrix splitting for area-preserving maps
and Hamiltonian systems with one and a half degrees of freedom. Special attention is paid …

Resonances are ubiquitous in dynamical systems with many degrees of freedom. They have
the basic effect of introducing slow-fast behavior in an evolutionary system which, coupled …

During the last two decades, in several branches of science (water waves, crystal growth,
travelling waves in one dimensional lattices, splitting of separatrices,...) different problems …

In 1984 VF Lazutkin [Laz84, LST89] obtained an asymptotic formula for the separatrix
splitting angle for the standard map. The difficulty of this problem is related to the …

Page 1 |MEMOIRS Of the American Mathematical Society Number 775 On the Splitting of
Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems P. Lochak J.-P …

The result of Mather on the existence of trajectories with unbounded energy for time periodic
Hamiltonian systems on a torus is generalized to a class of multi-dimensional Hamiltonian …

We deal with a perturbation of a hyperbolic integrable Hamiltonian system with n+ 1 degrees
of freedom. The integrable system is assumed to have n-dimensional hyperbolic invariant …

The splitting of separatrices for Hamiltonians with 11 2 degrees of freedom h (x; t=")= h0
(x)+" ph1 (x; t=") is measured. We assume that h0 (x)= h0 (x1; x2)= x2 2= 2+ V (x1) has a …

We study the problem of exponentially small splitting of separatrices of one degree of
freedom classical Hamiltonian systems with a non-autonomous perturbation fast and …

We assume that a symplectic real-analytic map has an invariant normally hyperbolic cylinder
and an associated transverse homoclinic cylinder. We prove that generically in the real …