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Lyapunov minimizing measures for expanding maps of the circle
We consider the set of maps f\in\mathcal{F}_{\alpha+} = \cup_{\beta>\alpha} \mathcal{C}^{1+\beta} of the circle which are covering maps of degree D, expanding, \min_{x\in S^1}f'(x) >1 and orientationExpand
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An invariant measure for rational maps
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Entropy and variational principle for one-dimensional lattice systems with a general a priori probability: positive and zero temperature
We generalize several results of the classical theory of thermodynamic formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^{\mathbb{N}}$ andExpand
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The theta group and the continued fraction expansion with even partial quotients
F. Schweiger introduced the continued fraction with even partial quotients. We will show a relation between closed geodesics for the theta group (the subgroup of the modular group generated by z+2Expand
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Exact bounds for the polynomial decay of correlation, 1/f noise and the CLT for the equilibrium state of a non-Hölder potential
We analyse the correlation and limit behaviour of partial sums for the stationary stochastic process (f(Tt(x)),µ),t = 0,1,..., for functions f of superpolynomial variation, the class defined belowExpand
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Ruelle Operator for Continuous Potentials and DLR-Gibbs Measures
In this work we study the Ruelle Operator associated to a continuous potential defined on a countable product of a compact metric space. We prove a generalization of Bowen's criterion for theExpand
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Equilibrium measures for rational maps
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Ergodic optimization, zero temperature limits and the max-plus algebra
Lecture notes of a course at the Brazilian Mathematical Colloquium. We review some basic notions in ergodic theory and thermodynamic formalism, as well as introductory results in the context ofExpand
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Entropy and large deviation
The author shows the existence of a deviation function for the maximal measure mu of a hyperbolic rational map of degree d. He relates several results of large deviation with the thermodynamicExpand
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The dimension spectrum of the maximal measure
A variety of complicated fractal objects and strange sets appears in nonlinear physics. In diffusion-limited aggregation, the probability of a random walker landing next to a given site of theExpand
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