CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

25 août 2020 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems

Séminaire par Maxime Breden (École Polytechnique, France), Maximilian Engel (Freie Universität Berlin, Germany)

In this talk, we discuss a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains, we reformulate the problem into the rigorous computation of eigenvectors of some elliptic PDEs, namely the Kolmogorov/Fokker-Planck equations describing distributions of the underlying stochastic process, and are thus able to prove that  the first Lyapunov exponent is positive for certain parameter regimes.