Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems
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DOI：
10.1214/22-aap1841
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发表时间：
2021-01
期刊：
影响因子：
--
通讯作者：
M. Breden;Maximilian Engel
中科院分区：
文献类型：
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作者：
M. Breden;Maximilian Engel
我们证实了一个长期存在的猜想剪切诱导混沌随机扰动系统表现出的Hopf分岔。给出了一个正的李雅普诺夫指数，这是一个计算机辅助证明。利用最近发展的有界域上的条件李雅普诺夫指数理论和修正的Furstenberg-Khasminskii公式，问题归结为描述基本随机过程分布的Kolmogorov算子的本征函数的严格计算。
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.