DNA-seminarium: Stationary phase methods and the splitting of separatrices
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 12167
- Lecturer: Alejandro Luque
- Contact person: Anders Öberg
Abstract: In this talk we discuss the splitting of separatrices (homoclinic chaos) under rapidly oscillating (in time and space) perturbations. 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 related to a priori stable systems with low regularity perturbations. They model also wave-type perturbations that arise in the study of the motion of charged particles in a rapidly oscillating electromagnetic field.