Artur O. Lopes

ORCID: 0000-0003-2040-4603
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About
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Research Areas
  • Mathematical Dynamics and Fractals
  • Quantum chaos and dynamical systems
  • Advanced Thermodynamics and Statistical Mechanics
  • Theoretical and Computational Physics
  • Statistical Mechanics and Entropy
  • Markov Chains and Monte Carlo Methods
  • Stochastic processes and statistical mechanics
  • Quantum Mechanics and Applications
  • Advanced Operator Algebra Research
  • Advanced Topology and Set Theory
  • advanced mathematical theories
  • Geometric Analysis and Curvature Flows
  • Stochastic processes and financial applications
  • Complex Systems and Time Series Analysis
  • Chaos control and synchronization
  • Advanced Differential Equations and Dynamical Systems
  • Cellular Automata and Applications
  • Geometry and complex manifolds
  • Advanced Mathematical Theories and Applications
  • Nonlinear Dynamics and Pattern Formation
  • Advanced Topics in Algebra
  • Functional Equations Stability Results
  • Quantum Computing Algorithms and Architecture
  • Advanced Banach Space Theory
  • Quantum many-body systems

Universidade Federal do Rio Grande do Sul
2015-2024

Brazilian Institute of Geography and Statistics
2015-2024

Institute of Mathematical Sciences
2006-2015

Universidade Federal de Uberlândia
2015

Universidade do Vale do Itajaí
2014

National Council for Scientific and Technological Development
2011

Universidade Federal de Minas Gerais
2011

University of Aveiro
2011

Universidade Federal de Santa Catarina
2010

University of Maryland, College Park
1988-1998

10.1007/bf02584744 article EN Boletim da Sociedade Brasileira de Matemática 1983-03-01

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...

10.1017/s0143385701001663 article EN Ergodic Theory and Dynamical Systems 2001-10-01

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...

10.1017/etds.2014.15 article EN Ergodic Theory and Dynamical Systems 2014-07-03

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...

10.1088/0951-7715/3/2/013 article EN Nonlinearity 1990-05-01

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...

10.1137/0520081 article EN SIAM Journal on Mathematical Analysis 1989-09-01

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...

10.1017/s0143385707000491 article EN Ergodic Theory and Dynamical Systems 2008-01-17

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.

10.48550/arxiv.1305.2396 preprint EN other-oa arXiv (Cornell University) 2013-01-01

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...

10.55905/rdelosv18.n65-119 article PT cc-by-nc DELOS Desarrollo Local Sostenible 2025-03-27

10.1006/aima.1993.1045 article EN publisher-specific-oa Advances in Mathematics 1993-10-01

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.

10.1142/s0219493706001657 article EN Stochastics and Dynamics 2006-03-01

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...

10.4171/jems/814 article EN Journal of the European Mathematical Society 2018-07-09

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...

10.1137/s0036139995279433 article EN SIAM Journal on Applied Mathematics 1996-04-01

10.1007/s00574-009-0028-6 article EN Bulletin of the Brazilian Mathematical Society New Series 2009-11-09

10.1007/s00574-009-0001-4 article EN Bulletin of the Brazilian Mathematical Society New Series 2009-03-01

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.

10.1142/s0219493712500050 article EN Stochastics and Dynamics 2012-05-22

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.,...

10.1137/110826333 article EN SIAM Journal on Applied Dynamical Systems 2012-01-01

10.1007/s10955-012-0626-3 article EN Journal of Statistical Physics 2012-11-01

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...

10.3934/dcds.2017264 article EN Discrete and Continuous Dynamical Systems 2017-01-01

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.

10.1088/0951-7715/28/11/4117 article EN Nonlinearity 2015-10-01
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