Geometry Seminar
Splitting of separatrices in generalized standard maps
Speaker: Didac Gil (UPC)Date: Wednesday, 28 January 2026 - 11:30Place: Aula Naranja, ICMAT
Abstract:
We study transversal intersections between the invariant manifolds (stable and unstable) associated to a hyperbolic fixed point for a class of maps named generalized standard maps. This generalization includes the Standard map, first studied by Lazutkin, the perturbed McMillan map or the Hénon map among others. We obtain an asymptotic formula for the Lazutkin invariant, a value related to the angle of intersection between the manifolds, which is exponentially small, and its first term depends on a Stokes constant. To do so, one of the techniques that we use is the inner equation related to the considered maps. Joint work with Inmaculada Baldomà (UPC), Maciej Capinski (AGH) and Pau Martín (UPC).
