We consider the set of maps f\in\mathcal{F}_{\alpha+} = \cup_{\beta>\alpha} \mathcal{C}^{1+\beta} circle which are covering degree D, expanding, \min_{x\in S^1}f'(x) >1 and orientation preserving. interested in characterizing such f admit a unique f-invariant probability measure \mu minimizing \int \ln f'\,d\mu over all measures. show there exists \mathcal{G}_+\subset\mathcal{F}_{\alpha+}, open dense \mathcal{C}^{1+\alpha}-topology, admitting supported on periodic orbit. also that, if admits...

We generalize several results of the classical theory Thermodynamic Formalism by considering a compact metric space $M$ as state space. analyze shift acting on $M^\mathbb{N}$ and consider general a-priori probability for defining Transfer (Ruelle) operator. study potentials $A$ which can depend infinite set coordinates in $M^\mathbb{N}.$ define entropy its very nature it is always nonpositive number. The concepts transfer operator are linked. If M not finite there exist Gibbs states with...

The author shows the existence of a deviation function for maximal measure mu hyperbolic rational map degree d. He relates several results large with thermodynamic formalism ergodic theory. plays distinguished role among other invariant measures, because stochastic process given by and will generate free energy function, whose Legendre transform in set measures be log d minus entropy sense Shannon-Kolmogorov. This result is associated relation between pressure energy. A general description...

A variety of complicated fractal objects and strange sets appears in nonlinear physics. In diffusion-limited aggregation, the probability a random walker landing next to given site aggregate is interest. percolation, distribution voltages across different elements random-resistor network (see [T. Halsey et al., Phys. Rev. (3), 33 (1986), pp. 1141–1151]) may be These examples can better analyzed by dividing certain pieces labeled indexes, but that leads working with notion dimension [Halsey...

Abstract We propose a new model of ergodic optimization for expanding dynamical systems: the holonomic setting. In fact, we introduce an extension standard used in this theory. The formulation consider here is quite natural if one wants meaning possible variations real trajectory under forward shift. other contexts (for twist maps, instance), property appears crucial way. A version Aubry–Mather theory symbolic dynamics introduced. are mainly interested problems related to properties...

Lecture notes of a course at the Brazilian Mathematical Colloquium. We review some basic notions in ergodic theory and thermodynamic formalism, as well introductory results context max-plus algebra, order to exhibit properties equilibrium measures when temperature goes zero.

Objetivo: Verificar, na literatura científica, estratégias terapêuticas eficazes para o tratamento de disfunções mitocondriais relacionadas à obesidade e Diabetes Mellitus Tipo 2 (DM2). Métodos: Consiste em uma revisão integrativa cunho descritivo exploratório com artigos publicados entre 2019 a 2024, no idioma português inglês texto completo disponível. Foi utilizada como questão norteadora: Quais são restabelecer função mitocondrial DM2 obesidade? A busca bibliografia foi efetuada outubro...

Consider a α-Hölder function A : Σ → ℝ and assume that it admits unique maximizing measure μ max . For each β, we denote β , the equilibrium associated to βA. We show (μ ) satisfies Large Deviation Principle, is, for any cylinder C of Σ, [Formula: see text] where V(x) is strict subaction A.

Given an onto map T acting on a metric space \Omega and appropriate Banach of functions \mathcal X(\Omega) , one classically constructs for each potential A \in X transfer operator \mathscr L_A . Under suitable hypotheses, it is well-known that has maximal eigenvalue \lambda_A spectral gap defines unique Gibbs measure \mu_A Moreover there normalized the form B=A+f-f\circ T+c as representative class all potentials defining same measure. The goal present article to study geometry set N...

Billiards are the simplest models for understanding statistical theory of dynamics a gas in closed compartment. We analyze class billiards (the open billiard on plane) terms invariant and conditionally probabilities. The dynamical system has horseshoe structure. stable unstable manifolds analytically described. natural probability $\mu $ is support Cantor set. This conditional limit _F that density with respect to Lebesgue measure. A formula relating entropy, Lyapunov exponent, Hausdorff...

For the shift σ in Σ = {0, 1} ℕ , we define renormalization for potentials by [Formula: see text] We show that a good H, there is unique fixed point text]. It Hofbauer potential V*. stable set of potential, i. e. V such converges to V* characterized germ these close 0 ∞ 000…. Then, make connections with Manneville–Pomeau map f : [0, 1]↺. In particular lift log f′ second part, characterize "good" 2 ◦ H σ. last study thermodynamic formalism some special They are called virtual maps.

For the subshift of finite type $\Sigma=\{0,1,2\}^{\mathbb{N}}$ we study convergence and selection at temperature zero Gibbs measure associated to a non–locally constant Hölder potential which admits exactly two maximizing ergodic measures. These measures are Dirac different fixed points, is flatter one these points. We prove that there always but not necessarily point where flattest. This contrary what was expected in light analogous problem Aubry-Mather theory [N. Anantharaman et al.,...

In this paper, we describe several different meanings for the concept of Gibbs measure on lattice $\mathbb{N}$ in context finite alphabets (or state space). We compare and analyze these ''in principle' distinct notions: DLR-Gibbs measures, Thermodynamic Limit eigenprobabilities dual Ruelle operator (also called conformal measures).Among other things extended classical notion a Gibbsian specification such way that similarity many results Statistical Mechanics Dynamical System becomes...

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.