Related papers: Gibbs measures have local product structure
In this paper, we study physical measures for partially hyperbolic diffeomorphisms with multi one-dimensional centers under the condition that all Gibbs $u$-states are hyperbolic. We prove the finiteness of ergodic physical measures. Then…
We study the $u$-Gibbs measures of a certain class of uniformly hyperbolic skew products on $\mathbb{T}^4$. These systems have a strong unstable and a weak unstable directions. We show that $C^r$-dense and $C^2$-open in this set every…
We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamical formalism for generalized Gibbs states will be discussed. A new class of…
We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique" Gibbs measures for which the same results can…
We obtain new entropy rigidity results for $u$-Gibbs measures by showing that whenever a $u$-Gibbs measure of a partially hyperbolic diffeomorphism admits an unstable Margulis family, the unstable Jacobian data of the system must to be…
The robustness of properties of a statistical physics model to slight perturbations in the exact local interactions of the model is a very relevant philosophical question, considering real-life measurements on which we base some models can…
We study a class of strongly irreducible, multidimensional, topological Markov shifts, comparing two notions of "symmetric measure": exchangeability and the Gibbs (or conformal) property. We show that equilibrium measures for such shifts…
We introduce two properties, macroscopic mixing and transitive mixing, to represent the macroscopic stability of time evolution of Gibbs measures. We claim that these are fundamental properties of macroscopic systems that exhibit relaxation…
With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities)…
The multifractal formalism for measures hold whenever the existence of corresponding Gibbs-like measures supported on the singularities sets holds. In the present work we tried to relax such a hypothesis and introduce a more general…
We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of ``almost Gibbsian measures'' (almost sure continuity…
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…
Concerns are expressed for the Monotonic Imbalance Bounding (MIB) property (Iacus et al. 2011) and for MIB matching because i) the definition of the MIB property leads to inconsistencies and the nature of the imbalance measure is not…
In this paper we obtain $C^2$-open sets of dissipative, partially hyperbolic skew products having a unique SRB measure with full support and full basin. These partially hyperbolic systems have a two dimensional center bundle which presents…
We consider the local dimension spectrum of a weak Gibbs measure on a C^1 non-uniformly hyperbolic system of Manneville- Pomeau type. We present the spectrum in three ways: using invariant measures, uniformly hyperbolic ergodic measures and…
In this article we will describe a new construction for Gibbs measures for hyperbolic attractors generalizing the original construction of Sinai, Bowen and Ruelle of SRB measures. The classical construction of the SRB measure is based on…
We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability…
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…
We study images of equilibrium (Gibbs) states for a class of non-invertible transformations associated to conformal iterated function systems with overlaps $\mathcal S$. We prove exact dimensionality for these image measures, and find a…
We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we…