On the Statistical Stability of Families of Attracting Sets and the Contracting Lorenz Attractor
On the Statistical Stability of Families of Attracting Sets and the Contracting Lorenz Attractor
复制标题
论吸引集族和收缩洛伦兹吸引子的统计稳定性
DOI：
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发表时间：
2020
影响因子：
1.6
通讯作者：
V. Araújo
中科院分区：
文献类型：
--
作者：
V. Araújo
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 C2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{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.
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 C2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{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.