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Estimating invariant measures and Lyapunov exponents

Published online by Cambridge University Press:  19 September 2008

Brian R. Hunt
Brian R. Hunt
Affiliation:
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA (e-mail: bhunt@ipst.umd.edu)
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Abstract

This paper describes a method for obtaining rigorous numerical bounds on time averages for a class of one-dimensional expanding maps. The idea is to directly estimate the absolutely continuous invariant measure for these maps, without computing trajectories. The main theoretical result is a bound on the convergence rate of the Frobenius—Perron operator for such maps. The method is applied to estimate the Lyapunov exponents for a planar map of recent interest.

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Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996, pp. 735 - 749
Copyright
Copyright © Cambridge University Press 1996

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