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We confirm a long-standing conjecture concerning shear-induced chaos instochastically perturbed systems exhibiting a Hopf bifurcation. The method ofshowing the main chaotic property, a positive Lyapunov exponent, is acomputer-assisted proof. Using the recently developed theory of conditionedLyapunov exponents on bounded domains and the modified Furstenberg-Khasminskiiformula, the problem boils down to the rigorous computation of eigenfunctionsof the Kolmogorov operators describing distributions of the underlyingstochastic process.

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