Equilibrium states for piecewise monotonic transformations
- 1 March 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 2 (1) , 23-43
- https://doi.org/10.1017/s014338570000955x
Abstract
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.Keywords
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