Related papers: Beyond Bowen's Specification Property
We review the inherent structure thermodynamical formalism and the formulation of an equation of state for liquids in equilibrium based on the (volume) derivatives of the statistical properties of the potential energy surface. We also show…
We study the thermodynamic formalism of systems where the potential depends randomly on an exterior system. We define the {\em pressure out of equilibrium} for such a family of potentials, and prove a corresponding variational principle. We…
We study the thermodynamic formalism of sufficiently regular interval maps for Holder continuous potentials. We show that for a hyperbolic potential there is a unique equilibrium state, and that this measure is exponentially mixing.…
We study the existence and uniqueness of equilibrium states for continuous flows on a compact, locally maximal invariant set under weak, non-uniform versions of specification, expansivity, and the Bowen property, further improving the…
In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full…
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…
It is given notions of singular hyperbolicity and sectional Lyapunov exponents of orders beyond the classical ones, namely, other dimensions besides the dimension 2 and the full dimension of the central subbundle of the singular hyperbolic…
This text provides an overview of the (geometric) thermodynamic formalism for transcendental meromorphic and entire functions with particular emphasis on geometric/fractal aspects such as Bowen's Formula expressing the hyperbolic dimension…
In [44], we qualitatively studied some classical results implied by the specification property for dynamical systems with non-uniform specification. In this paper, we perform quantitative studies on how properties of topological theory and…
In this work, we study ergodic properties of certain partially hyperbolic attractors whose central direction has a neutral behavior, the main feature is a condition of transversality between unstable leaves when projected by the stable…
It is well-known that SRB and equilibrium measures for uniformly hyperbolic flows admit a product structure in terms of measures on stable and unstable leaves with scaling properties given by the potential function. We describe a…
In this paper, we derive a local unique continuation property for stochastic hyperbolic equations without boundary conditions. This result is proved by a global Carleman estimate.
This paper gives a concise, mathematically rigorous description of phenomenological equilibrium thermodynamics for single-phase systems in the absence of chemical reactions and external forces. The present approach is similar to that of…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
In this article, we investigate the Variational Principle and develop thermodynamic formalism for correspondences. We define the measure-theoretic entropy for transition probability kernels and topological pressure for correspondences.…
We propose a generalized thermodynamics in which quasi-homogeneity of the thermodynamic potentials plays a fundamental role. This thermodynamic formalism arises from a generalization of the approach presented in paper [1], and it is based…
We obtain a characterization of two classes of dynamics with nonuniformly hyperbolic behavior in terms of an admissibility property. Namely, we consider exponential dichotomies with respect to a sequence of norms and nonuniformly hyperbolic…
We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…
We obtain limit theorems (Stable Laws and Central Limit Theorems, both Gaussian and non-Gaussian) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The proofs of the limit…
Isolated quantum systems in extreme conditions can exhibit unusually large occupancies per mode. This over-population gives rise to new universality classes of many-body systems far from equilibrium. We present theoretical evidence that…