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Computing Invariant Densities and Metric Entropy

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.¶E-mail: mp@ma.man.ac.uk, , , , , , UK

    Mark Pollicott

  2. 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

    Oliver Jenkinson

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  1. Mark Pollicott
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  2. Oliver Jenkinson
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Received: 25 July 1999 / Accepted: 7 January 2000

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Pollicott, M., Jenkinson, O. Computing Invariant Densities and Metric Entropy. Comm Math Phys 211, 687–703 (2000). https://doi.org/10.1007/s002200050832

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  • DOI: https://doi.org/10.1007/s002200050832

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