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Why escape is faster than expected
Journal of Physics A: Mathematical and Theoretical ( IF 2.1 ) Pub Date : 2020-10-07 , DOI: 10.1088/1751-8121/abb7bc
Hassan Attarchi , Leonid A Bunimovich

We consider chaotic (hyperbolic) dynamical systems which have a generating Markov partition. Then, open dynamical systems are built by making one element of a Markov partition a ‘hole’ through which orbits escape. We compare various estimates of the escape rate which correspond to a physical picture of leaking in the entire phase space. Moreover, we uncover a reason why the escape rate is faster than expected, which is the convexity of the function defining escape rate. Exact computations are present for the skewed tent map and Arnold’s cat map.



中文翻译:

为什么逃跑比预期的要快

我们考虑具有生成马尔可夫分区的混沌(双曲线)动力系统。然后,通过使马尔可夫分区的一个元素成为轨道逃逸的“洞”来构建开放动力系统。我们比较了逃逸率的各种估计,这些估计对应于整个相空间中泄漏的物理图片。此外,我们发现了逃逸率比预期快的一个原因,即定义逃逸率的函数的凸性。倾斜的帐篷地图和阿诺德的猫地图都有精确的计算。

更新日期:2020-10-07
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