Speaker
Description
Aubry and Mather sets describe the invariant structures selected by action minimization in Hamiltonian dynamics. Their computation is particularly relevant in celestial mechanics, where resonances and transitions between regular and chaotic motion create intricate dynamical patterns that are difficult to detect using trajectories alone.
In this talk, I will present joint work with Fabio Camilli on semi-discrete and fully discrete approximations of these sets. Our approach combines discrete Lax–Oleinik operators with a finite-dimensional variational formulation for minimizing measures. The resulting schemes approximate critical values, weak KAM solutions, and the supports of invariant minimizing measures, while preserving the variational structure of the continuous problem.
I will also discuss the numerical challenges created by multiple minimizing components and outline how calibration defects and structure-preserving learning may help identify the variational skeleton of resonant Hamiltonian systems.