• DOI:10.1017/S014338570000955X
• Corpus ID: 84178444

Equilibrium states for piecewise monotonic transformations

@article{Hofbauer1982EquilibriumSF,
  title={Equilibrium states for piecewise monotonic transformations},
  author={Franz Hofbauer and Gerhard Keller},
  journal={Ergodic Theory and Dynamical Systems},
  year={1982},
  volume={2},
  pages={23 - 43}
}

• F. Hofbauer, G. Keller
• Published 1 March 1982
• Physics, Mathematics
• Ergodic Theory and Dynamical Systems

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.