Memory loss for nonequilibrium open dynamical systems

Anushaya Mohapatra; William Ott

doi:10.3934/dcds.2014.34.3747

Article Contents

2014, Volume 34, Issue 9: 3747-3759. Doi: 10.3934/dcds.2014.34.3747

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Memory loss for nonequilibrium open dynamical systems

Anushaya Mohapatra^1, and
William Ott^1,

1.
Department of Mathematics, University of Houston, 651 PGH Hall, Houston, TX 77204

Received: February 28, 2013

Revised: November 30, 2013

Published: August 2014

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Abstract

We introduce a notion of conditional memory loss for nonequilibrium open dynamical systems. We prove that this type of memory loss occurs at an exponential rate for nonequilibrium open systems generated by one-dimensional piecewise-differentiable expanding Lasota-Yorke maps. This result may be viewed as a prototype for time-dependent dynamical systems with holes.

Keywords:

Mathematics Subject Classification: 37A25, 37C30, 37C60, 37D20, 37E05, 82C99.

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