# PDE och tillämpningar

- Date:
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
- Lecturer: Alejandro Luque, Uppsala: Oscillatory integrals and the problem of splitting of separatrices Benny Avelin, Uppsala: Oscillatory integrals and the problem of splitting of separatrices
- Contact person: Kaj Nyström
- Seminarium

10.15: Alejandro Luque, Uppsala: *Oscillatory integrals and the problem of splitting of separatrices*

*Abstract: *A fundamental problem in Dynamical Systems is to ascertain whether a given system is chaotic. One of the main tools to address this question, which dates back to Poincare, is to consider perturbations of a homoclinic connection of the system to produce transverse intersections of a stable manifold and an unstable manifold. The displacement (and hence the splitting) of such manifolds is typically approximated using an oscillatory integral called the Melnikov function. In this talk, we study the Melnikov function of a mechanical system that presents fast oscillations in time and space. Using stationary phase methods and the geometric constrains of the problem, we provide an explicit formula for the splitting which is valid in a very general setting.

11.15: Benny Avelin, Uppsala: *Introduction to deep learning, continued*