ALLA SCOPERTA DI SCHEMI NASCOSTI NELLE DINAMICHE COMPLESSE: DAL PROBLEMA DEGLI N-CORPI ALLE RETI NEURALI (E RITORNO)

Abstract

In this note, we present the theoretical and computational approach our research group is developing to detect chaotic behaviours in the classical N-body problem of Celestial Mechanics. Inspired by the famous Poincaré conjecture, we numerically determine large sets of symmetric periodic orbits and we encode their simple motions by revealing the existence of a symbolic dynamics. Finally, we explore a new idea for combining periodic orbits to create new solutions with increasing complexity, using AI algorithms. We also revisit Conley’s ideas on low-energy transport orbits.