COMPUTER-ASSISTED PROOF OF SHEAR-INDUCED CHAOS IN STOCHASTICALLY PERTURBED HOPF SYSTEMS

• 成果类型: Article
• 署名作者: Breden, Maxime; Engel, Maximilian
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Free University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1841
• 发表日期: 2023
• 页码: 1052-1094
• 关键词: numerical verification; EXISTENCE

摘要

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.