Related papers: Thermodynamic formalism for contracting Lorenz flo…
We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…
We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for…
In this note we study the thermodynamic formalism for the positive geodesic flow on the modular surface. We define the pressure and prove the variational principle. We also establish conditions for the the pressure to be real analytic and…
We develop a Thermodynamic Formalism for bounded continuous potentials defined on the sequence space $X\equiv E^{\mathbb{N}}$, where $E$ is a general Borel standard space. In particular, we introduce meaningful concepts of entropy and…
In this note, we consider the thermodynamic formalism for Lorenz attractors of flows in any dimension. Under a mild condition on the H\"older continuous potential function $\phi$, we prove that for an open and dense subset of $C^1$ vector…
Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusion remains true using weaker non-uniform…
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 consider one parameter families of vector fields introduced by Rovella, obtained through modifying the eigenvalues of the geometric Lorenz attractor, replacing the expanding condition on the eigenvalues of the singularity by a…
We develop a non-extensive thermodynamic formalism for the one-sided shift on a finite alphabet, inspired by Tsallis' generalization of Boltzmann entropy in statistical physics. We introduce notions of $q$-entropy, $q$-pressure, and…
This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function…
Looking for the underlying hydrodynamic mechanisms determining the elliptic flow we show that for an expanding relativistic perfect fluid the transverse flow may derive from a solvable hydrodynamic potential, if the entropy is transversally…
We review the key steps of the relativistic fluid dynamics formalism with spin degrees of freedom initiated recently. We obtain equations of motion of the expansion of the system from the underlying definitions of quantum kinetic theory for…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…
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 infinity, the topological and the measure theoretic entropy…
This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium…
We present the full thermodynamics of a fluid confined by an arbitrary external potential based on the virial expansion of the grand potential. The fluid may be classical or quantum and it is assumed that interatomic interactions are…
We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…
We give necessary and sufficient conditions for the existence of smooth Lyapunov 1-forms for the flow of a smooth vector field in terms of the behavior of certain locally finite invariant measures. The main statement generalizes a result of…
The classical Lorenz flow, and any flow which is close to it in the $C^2$-topology, satisfies a Central Limit Theorem (CLT). We prove that the variance in the CLT varies continuously.
We use entropy theory as a new tool for studying Lorenz-like classes of flows in any dimension. More precisely, we show that every Lorenz-like class is entropy expansive, and has positive entropy which varies continuously with vector…