Théorique, numérique
The dynamics of chaotic systems exhibit an extreme sensitivity to initial conditions. Even the slightest variations between initially close trajectories lead to exponential separation over time, rendering long-term predictions exceedingly challenging. A famous example is the long-term motion of the inner planets in the Solar System. Despite the deterministic nature of these systems, their behavior ultimately evolves into a state of actual randomness on long time scales. Consequently, it becomes necessary to establish a statistical description, framed in terms of a probability density defined over the phase space of the dynamics. In the conventional Monte Carlo approach, the probability density of physical observables is estimated from a large ensemble of numerical integrations of the equations of motion. The internship opportunity presented here aims to explore an alternative approach to address the probabilistic description of chaotic dynamics.