Operator renewal theory for continuous time dynamical systems with finite and infinite measure

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• 作者：Ian Melbourne ; Dalia Terhesiu
• 关键词：Infinite ergodic theory ; Continuous time operator renewal equation ; Mixing rates
• 刊名：Monatshefte für Mathematik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：182
• 期：2
• 页码：377-431
• 全文大小：
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：182

文摘

We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over parabolic rational maps of the complex plane, and nonuniformly expanding semiflows with indifferent periodic orbits. In the finite measure case, the emphasis is on obtaining sharp rates of decorrelations, extending results of Gouëzel and Sarig from the discrete time setting to continuous time. In the infinite measure case, the primary question is to prove results on mixing itself, extending our results in the discrete time setting. In some cases, we obtain also higher order asymptotics and rates of mixing.