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Thermodynamical formalism for robust classes of potentials and non-uniformly hyperbolic maps

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  • Published online: 01 April 2008

We develop a Ruelle–Perron–Fröbenius transfer operator approach to the ergodic theory of a large class of non-uniformly expanding transformations on compact manifolds. For Hölder continuous potentials not too far from constant, we prove that the transfer operator has a positive eigenfunction, which is piecewise Hölder continuous, and use this fact to show that there is exactly one equilibrium state. Moreover, the equilibrium state is a non-lacunary Gibbs measure, a non-uniform version of the classical notion of Gibbs measure that we introduce here.

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Ergodic Theory and Dynamical Systems
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  • EISSN: 1469-4417
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