• Corpus ID: 244709364

A Ruelle-Perron-Frobenius theorem for expanding circle maps with an indifferent fixed point

@inproceedings{Garibaldi2021ART,
  title={A Ruelle-Perron-Frobenius theorem for expanding circle maps with an indifferent fixed point},
  author={Eduardo Garibaldi and Irene Inoquio-Renteria},
  year={2021}
}
In this note, we establish an original result for the thermodynamic formalism in the context of expanding circle transformations with an indifferent fixed point. For an observable whose continuity modulus is linked to the dynamics near such a fixed point, by identifying an appropriate linear space to evaluate the action of the transfer operator, we show that there is a strictly positive eigenfunction associated with the maximal eigenvalue given as the exponential of the topological pressure… 

References

SHOWING 1-10 OF 21 REFERENCES
Dynamical obstruction to the existence of continuous sub-actions for interval maps with regularly varying property
In ergodic optimization theory, the existence of sub-actions is an important tool in the study of the so-called optimizing measures. For transformations with regularly varying property, we highlight
An optimal transportation approach to the decay of correlations for non-uniformly expanding maps
We consider the transfer operators of non-uniformly expanding maps for potentials of various regularity, and show that a specific property of potentials (‘flatness’) implies a Ruelle–Perron–Frobenius
Equilibrium States of Weakly Hyperbolic One-Dimensional Maps for Hölder Potentials
There is a wealth of results in the literature on the thermodynamic formalism for potentials that are, in some sense, “hyperbolic”. We show that for a sufficiently regular one-dimensional map
Introduction to Ergodic theory
Hyperbolic dynamics studies the iteration of maps on sets with some type of Lipschitz structure used to measure distance. In a hyperbolic system, some directions are uniformly contracted and others
Equilibrium States for Interval Maps: Potentials with sup φ − inf φ < htop(f)
We study an inducing scheme approach for smooth interval maps to prove existence and uniqueness of equilibrium states for potentials φ with the ‘bounded range’ condition sup φ − inf φ < htop(f),
Conformal measure and decay of correlation for covering weighted systems
We show that for a large class of piecewise monotonic transformations on a totally ordered, compact set one can construct conformal measures and obtain the exponential mixing rate for the associated
Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a
Zeta functions and the periodic orbit structure of hyperbolic dynamics
© Société mathématique de France, 1990, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les
Equilibrium states for piecewise monotonic transformations
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
Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics
1. Introduction to the 2nd edition 2. Introduction 3. Theory of Gibbs States 4. Gibbs States: complements 5. Translation invariance: theory of equilibrium states 6. Connection between Gibbs States
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