2011/01/31 by Vitor Araujo, Vítor Araújo, Paulo Varandas · 19 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Attractor #Complex system #Exponential decay #Exponential dichotomy #Exponential function #Exponential growth #Gravitational singularity #Mathematical Dynamics and Fractals #Physical system #Stability and Controllability of Differential Equations #math-ph #math.DS #math.MP #msc:37A25 #msc:37C10 #msc:37D30
paper · pdf · doi:10.1007/s00220-012-1445-8
published in Communications in Mathematical Physics 311(1), 215-246 (Springer Science+Business Media) · Final version accepted for publication with added corrections (not in official published version) after O. Butterley pointed out to the authors that the last estimate in the argument in Subsection 4.2.3 of the previous version is not enough to guarantee the uniform non-integrability condition claimed. We have modified the argument and present it here in the same Subsection. 3 figures, 34 pages
openalex publication_date 2012/02/27 · arxiv created 2015/03/17 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We construct open sets of Ck (k bigger or equal to 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure.