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. 
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We consider a class of piecewise monotonically increasing functionsf on the unit intervalI. We want to determine the measures with maximal entropy for these transformations. In part I we construct a
The structure of piecewise monotonic transformations
  • F. Hofbauer
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 1981
Abstract Transformations on [0, 1] which are piecewise monotonic and piecewise continuous are considered. Using symbolic dynamics, the structure of their nonwandering set is determined. This is then
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