Why escape is faster than expected. (6th October 2020)

• Record Type: Journal Article
• Authors: Attarchi, Hassan; Bunimovich, Leonid A
• Is Part Of: Journal of physics. Volume 53:Number 43(2020)
• Publication Date: 2020-10-06
• Subjects: open dynamical systems -- escape rate -- Markov partition; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abb7bc
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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.