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

Maxime Breden; Maximilian Engel

doi:10.1214/22-AAP1841

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

Maxime Breden
, Maximilian Engel

École Polytechnique
Free University of Berlin

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	1052-1094
Nombre de pages	43
journal	Annals of Applied Probability
Volume	33
Numéro de publication	2
Les DOIs	https://doi.org/10.1214/22-AAP1841
état	Publié - 1 avr. 2023
Modification externe	Oui

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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.",

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AU - Engel, Maximilian

N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2023.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - 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.

AB - 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.

KW - Homotopy method

KW - Kolmogorov operators

KW - Lyapunov exponents

KW - quasi-ergodic distribution

UR - https://www.scopus.com/pages/publications/85153715959

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JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 2

ER -

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

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