Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
Résumé
We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted proof. Using the recently developed theory of conditioned Lyapunov exponents on bounded domains and the modified Furstenberg-Khasminskii formula, the problem boils down to the rigorous computation of eigenfunctions of the Kolmogorov operators describing distributions of the underlying stochastic process.
Mots clés
computer-assisted proof
homotopy method
Kolmogorov operators
Lyapunov exponents
quasi-ergodic distribution
shear-induced chaos
stochastic differential equations
computer-assisted proof homotopy method Kolmogorov operators Lyapunov exponents quasi-ergodic distribution shear-induced chaos stochastic differential equations. Mathematics Subject Classification (2020): 35P99 37-04 37M25 37H15 60J99
computer-assisted proof
stochastic differential equations. Mathematics Subject Classification (2020): 35P99
37-04
37M25
37H15
60J99
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