A closing scheme for finding almost-invariant sets in open dynamical systems
Gary Froyland - School of Mathematics and Statistics, 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.
Received: September 2011; Revised: June 2012; Available Online: April 2014.