| Abstract: |
| In this talk we discuss the splitting of separatrices under rapidly oscillating (in time and space) perturbations. These wave-type perturbations arise naturally in the study of the motion of charged particles in a rapidly oscillating electromagnetic field.
Using stationary phase methods, we provide an explicit formula for the asymptotic displacement of the invariant manifolds, which becomes algebraically small. Remarkably, the proof does not require any explicit knowledge of the separatrix and works also for non-analytic systems. As a corollary, we obtain positive topological entropy under generic conditions. The perturbations considered are also related to a priori stable systems with low regularity perturbations.
This is a joint work with Alberto Enciso and Daniel Peralta-Salas. |
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