TY - JOUR
AU - Araujo, Vitor
AB - We present criteria for statistical stability of attracting sets for vector fields using dynamical conditions on the corresponding generated flows. These conditions are easily verified for all singular-hyperbolic attracting sets of C2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C^2$$\end{document} vector fields using known results, providing robust examples of statistically stable singular attracting sets (encompassing in particular the Lorenz and geometrical Lorenz attractors). These conditions are shown to hold also on the persistent but non-robust family of contracting Lorenz flows (also known as Rovella attractors), providing examples of statistical stability among members of non-open families of dynamical systems. In both instances, our conditions avoid the use of detailed information about perturbations of the one-dimensional induced dynamics on specially chosen Poincaré sections.
TI - On the Statistical Stability of Families of Attracting Sets and the Contracting Lorenz Attractor
JF - Journal of Statistical Physics
DO - 10.1007/s10955-021-02729-x
DA - 2021-03-03
UR - https://www.deepdyve.com/lp/springer-journals/on-the-statistical-stability-of-families-of-attracting-sets-and-the-IKBagrSl4D
VL - 182
IS - 3
DP - DeepDyve
ER -