Computing Invariant Densities and Metric Entropy |
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| Authors: | Mark Pollicott Oliver Jenkinson |
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| Institution: | Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.?E-mail: mp@ma.man.ac.uk, UK
UPR 9016 CNRS, Institut de Mathématiques de Luminy, 163 avenue de Luminy, case 907, 13288 Marseille, cedex 9, France. E-mail: omj@iml.univ-mrs.fr, FR
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| Abstract: | We present a method for accurately computing the metric entropy (or, equivalently, the Lyapunov exponent) of the absolutely
continuous invariant measure μ for a piecewise analytic expanding Markov map T of the interval. We construct atomic signed measures μ
M
supported on periodic orbits up to period M, and prove that super-exponentially fast. We illustrate our method with several examples.
Received: 25 July 1999 / Accepted: 7 January 2000 |
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