Abstract
We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. Themethod 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.
| Original language | English |
|---|---|
| Pages (from-to) | 1052-1094 |
| Number of pages | 43 |
| Journal | Annals of Applied Probability |
| Volume | 33 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Apr 2023 |
| Externally published | Yes |
Keywords
- Homotopy method
- Kolmogorov operators
- Lyapunov exponents
- quasi-ergodic distribution