`a`
Journal of Computational Dynamics (JCD)
 

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

Pages: 135 - 162, Volume 1, Issue 1, June 2014      doi:10.3934/jcd.2014.1.135

 
       Abstract        References        Full Text (1584.7K)       Related Articles       

Gary Froyland - School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia (email)
Philip K. Pollett - School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072, Australia (email)
Robyn M. Stuart - School of Mathematics and Statistics, The University of New South Wales, Sydney NSW 2052, Australia (email)

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.

Keywords:  Open dynamical system, conditionally invariant measure, almostinvariant set, metastability, Perron-Frobenius operator, Ulam's method.
Mathematics Subject Classification:  Primary: 37M25; Secondary: 37A30.

Received: September 2011;      Revised: June 2012;      Available Online: April 2014.

 References