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Journal of Statistical Physics

, Volume 50, Issue 1–2, pp 213–229 | Cite as

A matrix method for estimating the Liapunov exponent of one-dimensional systems

  • Abraham Boyarsky
Articles

Abstract

Let τ: [0, 1]→[0, 1] be a piecewise monotonie expanding map. Then τ admits an absolutely continuous invariant measureμ. A result of Kosyakin and Sandler shows thatμ can be approximated by a sequence of absolutely continuous measuresμ n invariant under piecewise linear Markov maps τitn. Each τitn is constructed on the inverse images of the turning points of τ. The easily computable measuresμ n are used to estimate the Liapunov exponent of τ. The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.

Key words

Liapunov exponent piecewise monotonie map Markov map absolutely continuous univariant measure negative Schawarzian 

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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Abraham Boyarsky
    • 1
  1. 1.Department of Mathematics, Loyola CampusConcordia UniversityMontrealCanada

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