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Approximating invariant densities of metastable systems

Published online by Cambridge University Press:  02 September 2010

CECILIA GONZÁLEZ-TOKMAN ,
BRIAN R. HUNT  and
PAUL WRIGHT
CECILIA GONZÁLEZ-TOKMAN
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA (email: cecilia@math.umd.edu, paulrite@math.umd.edu)
BRIAN R. HUNT
Affiliation:
Department of Mathematics and Institute for Physical Sciences and Technology, University of Maryland, College Park, MD 20742, USA (email: bhunt@umd.edu)
PAUL WRIGHT
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA (email: cecilia@math.umd.edu, paulrite@math.umd.edu)
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Abstract

We consider a piecewise smooth expanding map on an interval which has two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed slightly to make the invariant sets merge, we describe how the unique ACIM of the perturbed map can be approximated by a convex combination of the two initial ergodic ACIMs. The result is generalized to the case of finitely many invariant components.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 5 , October 2011 , pp. 1345 - 1361
Copyright
Copyright © Cambridge University Press 2010

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