We give a proof based in geometric perturbation theory of a result proved by J. N. Mather using variational methods. Namely, the existence of orbits with unbounded energy in perturbations of a… (More)

We consider fast quasiperiodic perturbations with two frequencies (1 /ε, γ/ε) of a pendulum, whereγ is the golden mean number. The complete system has a twodimensional invariant torus in a… (More)

The linear oscillator equation with a frequency slowly dependent on time is used to test a method to compute exponentially small quantities. This work presents the matching method in the complex… (More)

We consider fast quasiperiodic perturbations with two frequencies (1="; =") of a pendulum, where is the golden mean number. The complete system has a two-dimensional invariant torus in a… (More)

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [5], their solutions were used in that article to measure an exponentially small separatrix… (More)

In this paper, we analytically consider sliding bifurcations of periodic orbits in the dry-friction oscillator. The system depends on two parameters: F , which corresponds to the intensity of the… (More)

We study the resurgent structure associated with a Hamilton Jacobi equation This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via… (More)

In this paper we study the exponentially small splitting of a heteroclinic connection in a one-parameter family of analytic vector fields in R3. This family arises from the conservative analytic… (More)