Rigorous enclosure of Lyapunov exponents of stochastic flows
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916768285458432 |
|---|---|
| author | Breden, Maxime Chu, Hugo Lamb, Jeroen S. W. Rasmussen, Martin |
| author_facet | Breden, Maxime Chu, Hugo Lamb, Jeroen S. W. Rasmussen, Martin |
| contents | We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the ergodicity of diffusion processes. We do not require any structural assumptions on the stochastic system and work under mild hypoellipticity conditions and outside of perturbative regimes. Therefore, our method allows for the treatment of systems that were so far out of reach from existing mathematical tools. We demonstrate our method to exhibit the chaotic nature of four different systems. Finally, we show the robustness of our approach by combining it with continuation methods to produce bounds on Lyapunov exponents over large parameter regions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigorous enclosure of Lyapunov exponents of stochastic flows Breden, Maxime Chu, Hugo Lamb, Jeroen S. W. Rasmussen, Martin Dynamical Systems Numerical Analysis Probability 37M25, 37H15, 65P30, 60J22, 65G20 We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the ergodicity of diffusion processes. We do not require any structural assumptions on the stochastic system and work under mild hypoellipticity conditions and outside of perturbative regimes. Therefore, our method allows for the treatment of systems that were so far out of reach from existing mathematical tools. We demonstrate our method to exhibit the chaotic nature of four different systems. Finally, we show the robustness of our approach by combining it with continuation methods to produce bounds on Lyapunov exponents over large parameter regions. |
| title | Rigorous enclosure of Lyapunov exponents of stochastic flows |
| topic | Dynamical Systems Numerical Analysis Probability 37M25, 37H15, 65P30, 60J22, 65G20 |
| url | https://arxiv.org/abs/2411.07064 |