We apply coupling techniques in order to prove that the transfer operators associated with random topological Markov chains and non-stationary shift spaces big images preimages property have a spectral gap.

We introduce a relative Gurevich pressure for random countabletopologically mixing Markov shifts. It is shown that the variationalprinciple holds this notion of pressure. also prove Ruelle-Perron-Frobenius theorem which enablesus to construct wealth invariant Gibbs measures locally fiber Hölder continuousfunctions. This accomplished via new construction an equivariantfamily using Crauel's Prohorov theorem. Someproperties are discussed as well.

We employ techniques from optimal transport in order to prove the decay of transfer operators associated with iterated functions systems and expanding maps, giving rise a new proof without requiring Doeblin–Fortet (or Lasota–Yorke) inequality.

We study a class of potentials $f$ on one sided full shift spaces over finite or countable alphabets, called product type. obtain explicit formulae for the leading eigenvalue, eigenfunction (which may be discontinuous) and eigenmeasure Ruelle operator. The uniqueness property these quantities is also discussed it shown that there always exists Bernoulli equilibrium state even if does not satisfy Bowen's condition. apply results to $f:\{-1,1\}^\mathbb{N} \to \mathbb{R}$ form $$...

In this work we study the Ruelle Operator associated to a continuous potential defined on countable product of compact metric space. We prove generalization Bowen's criterion for uniqueness eigenmeasures. One main results article is show that probability DLR-Gibbs (associated translation invariant specification), if and only if, an eigenprobability transpose operator. Bounded extensions operator Lebesgue space integrable functions, with respect eigenmeasures, are studied problem existence...

We introduce a relative notion of the 'big images and preimages'-property for random topological Markov chains. This then implies that version Ruelle-Perron-Frobenius theorem holds with respect to summable locally Hoelder continuous potentials.

We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $ X\equiv E^{\mathbb{N}} $, where E is general standard Borel space. In particular, we introduce meaningful concepts of entropy and pressure shifts acting X obtain existence equilibrium states as finitely additive probability measures any potential. Furthermore, establish convexity other structural properties set states, prove version Perron-Frobenius-Ruelle theorem under additional...

<p style='text-indent:20px;'>In this work we study the Ruelle Operator associated to a continuous potential defined on countable product of compact metric space. We prove generalization Bowen's criterion for uniqueness eigenmeasures and that one-sided one-dimensional DLR-Gibbs measures translation invariant specifications are transpose operator. From last claim one gets concept eigenprobability operator is equivalent DLR probability. style='text-indent:20px;'>Bounded extensions Lebesgue...

For a non-compact hyperbolic surface $M$ of finite area, we study certain Poincaré section for the geodesic flow. The canonical, non-invertible factor first return map to this is shown be pointwise dual ergodic with sequence $(a

We analyze the Lyapunov spectrum of relative Ruelle operator associated with a skew product whose base is an ergodic automorphism and fibers are full shifts. prove that these operators can be approximated in [Formula: see text]-topology by positive matrices dominated splitting.

Abstract We find generalized conformal measures and equilibrium states for random dynamics generated by Ruelle expanding maps, under which the exhibits exponential decay of correlations. This extends results Baladi [Correlation spectrum quenched annealed maps. Comm. Math. Phys. 186 (1997), 671–700] Carvalho et al [Semigroup actions J. Stat. 116 (1) (2017), 114–136], where randomness is driven an independent identically distributed process phase space assumed to be compact. give applications...

In this paper we describe the spectral properties of semigroups expanding maps acting on Polish spaces, considering both sequences transfer operators along infinite compositions dynamics and integrated operators. We prove that there exists a limiting behaviour for such operators, these semigroup actions admit equilibrium states with exponential decay correlations several limit theorems. The reformulation results in terms quenched annealed extend by Baladi (1997) Carvalho, Rodrigues &amp;...

In this paper we use infinite ergodic theory to study limit sets of essentially free Kleinian groups which may have parabolic elements arbitrary rank. By adapting a method Adler, construct section map S for the geodesic flow on associated hyperbolic manifold. We then show that has Markov property and it is conservative with respect invariant measure induced by Liouville–Patterson measure. Furthermore, obtain rationally different types return sequences (an), are governed exponent convergence...

We establish a law of the iterated logarithm (LIL) for set real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ sequence such that $\sum 1/\alpha_n$ finite. This shown to have Hausdorff dimension $1/2$ in many cases and measure LIL absolutely continuous measure. The result obtained as an application strong invariance principle unbounded observables on limit sequential function system.

Abstract In this paper we extend results concerning conservativity and the existence of σ -finite measures to random transformations which admit a countable relative Markov partition. We consider systems are locally fibre-preserving countable, If system is irreducible satisfies distortion property deduce that either totally dissipative or conservative ergodic. For systems, provide sufficient conditions for absolutely continuous invariant measures.