23 citations · 55 across the 10 of their papers we have counts for
17 papers
Pressure at infinity and Large Deviations
Godofredo Iommi, Thomas Jordan, Anibal Velozo
We establish level-1 large deviation principles for continuous time suspension flows over countable Markov shifts, a class of non compact dynamical systems. Our results both quanti…
Equidistribution and thermodynamics at infinity
Godofredo Iommi, Felipe Riquelme, Aníbal Velozo
We prove level-2 large deviation upper bounds for potentials on countable Markov shifts and for suspension semi-flows over countable Markov shifts. For strongly positive recurrent…
Non-compact spaces of invariant measures
Godofredo Iommi, Anibal Velozo
We study a compactification of the space of invariant probability measures for a transitive countable Markov shift. We prove that it is affine homeomorphic to the Poulsen simplex.…
Pressure at infinity on countable Markov shifts
Anibal Velozo
In this article, we study the pressure at infinity of potentials defined over countable Markov shifts. We establish an upper semi-continuity result concerning the limiting behaviou…
On the Hausdorff dimension of geodesics that diverge on average
Felipe Riquelme, Anibal Velozo
In this article we prove that the Hausdorff dimension of geodesic directions that are recurrent and diverge on average coincides with the entropy at infinity of the geodesic flow f…
Ergodic optimization and zero temperature limits in negative curvature
Felipe Riquelme, Anibal Velozo
In this paper we study aspects of the ergodic theory of the geodesic flow on a non-compact negatively curved manifold. It is a well known fact that every continuous potential on a…
Measures of maximal entropy for suspension flows
Godofredo Iommi, Anibal Velozo
We study suspension flows defined over sub-shifts of finite type with continuous roof functions. We prove the existence of suspension flows with uncountably many ergodic measures o…
Escape of entropy for countable Markov shifts
Godofredo Iommi, Mike Todd, Anibal Velozo
In this paper we study ergodic theory of countable Markov shifts. These are dynamical systems defined over non-compact spaces. Our main result relates the escape of mass, the measu…
The space of invariant measures for countable Markov shifts
Godofredo Iommi, Anibal Velozo
It is well known that the space of invariant probability measures for transitive sub-shifts of finite type is a Poulsen simplex. In this article we prove that in the non-compact se…
Upper semi-continuity of entropy in non-compact settings
Godofredo Iommi, Mike Todd, Aníbal Velozo
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to…
Pressure, Poincaré series and box dimension of the boundary
Godofredo Iommi, Aníbal Velozo
In this note we prove two related results. First, we show that for certain Markov interval maps with infinitely many branches the upper box dimension of the boundary can be read fr…
Thermodynamic formalism and the entropy at infinity of the geodesic flow
Anibal Velozo
In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at…
Rate distortion theory, metric mean dimension and measure theoretic entropy
Anibal Velozo, Renato Velozo
We prove a variational principle for the metric mean dimension analog to the one in [LT]. Instead of using the rate distortion function we use the function that is clo…
Phase transitions for geodesic flows and the geometric potential
Anibal Velozo
In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slo…
Semicontinuity of measure theoretic entropy for noncompact systems
Anibal Velozo
We prove the upper semicontinuity of the measure theoretic entropy for the geodesic flow on complete Riemannian manifolds without focal points and bounded sectional curvature. We t…
Escape of mass and entropy for geodesic flows
Felipe Riquelme, Anibal Velozo
In this paper we study the ergodic theory of the geodesic flow on negatively curved geometrically finite manifolds. We prove that the measure theoretic entropy is upper semicontinu…
Entropy in the cusp and phase transitions for geodesic flows
Godofredo Iommi, Felipe Riquelme, Anibal Velozo
In this paper we study the geodesic flow for a particular class of Riemannian non-compact manifolds with variable pinched negative sectional curvature. For a sequence of invariant…