CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

August 25, 2020 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

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

Seminar presented by 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.