A closing scheme for finding almost-invariant sets in open dynamical systems

Gary Froyland; Philip K. Pollett; Robyn M. Stuart

doi:10.3934/jcd.2014.1.135

Article Contents

2014, Volume 1, Issue 1: 135-162. Doi: 10.3934/jcd.2014.1.135

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A closing scheme for finding almost-invariant sets in open dynamical systems

1.
School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052
2.
School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072
3.
School of Mathematics and Statistics, The University of New South Wales, Sydney NSW 2052

Received: August 31, 2011

Revised: May 31, 2012

Published: December 2013

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Abstract

We explore the concept of metastability or almost-invariance in open dynamical systems. In such systems, the loss of mass through a ``hole'' occurs in the presence of metastability. We extend existing techniques for finding almost-invariant sets in closed systems to open systems by introducing a closing operation that has a small impact on the system's metastability.

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Mathematics Subject Classification: Primary: 37M25; Secondary: 37A30.

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