Fast–Slow Partially Hyperbolic Systems Versus Freidlin–Wentzell Random Systems

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• 作者：Jacopo de Simoi ; Carlangelo Liverani ; Christophe Poquet…
• 关键词：Averaging ; Metastability ; Partially hyperbolic ; Decay of correlations
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：166
• 期：3-4
• 页码：650-679
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Freidlin–Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a “sink” with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.