  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.
