Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems - Département de mathématiques appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems

Résumé

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.
Fichier principal
Vignette du fichier
submission_breden_engel.pdf (1.57 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03168199 , version 1 (12-03-2021)
hal-03168199 , version 2 (22-11-2023)

Identifiants

  • HAL Id : hal-03168199 , version 1

Citer

Maxime Breden, Maximilian Engel. Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems. 2021. ⟨hal-03168199v1⟩

Collections

HPCMATHS
90 Consultations
60 Téléchargements

Partager

Gmail Facebook X LinkedIn More