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Equilibrium states for piecewise monotonic transformations

Published online by Cambridge University Press:  13 August 2009

Franz Hofbauer  and
Gerhard Keller
Franz Hofbauer
Affiliation:
Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien
Gerhard Keller
Affiliation:
Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900 Heidelberg
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Abstract

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We show that equilibrium states μ of a function φ on ([0,1], T), where T is piecewise monotonic, have strong ergodic properties in the following three cases:

(i) sup φ — inf φ <htop(T) and φ is of bounded variation.

(ii) φ satisfies a variation condition and T has a local specification property.

(iii) φ = —log |T′|, which gives an absolutely continuous μ, T is C2, the orbits of the critical points of T are finite, and all periodic orbits of T are uniformly repelling.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 1 , March 1982 , pp. 23 - 43
Copyright
Copyright © Cambridge University Press 1982

References

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