THE POTENTIAL POINT OF VIEW FOR RENORMALIZATION

DOI10.1142/S0219493712500050zbMath1268.37057OpenAlexW2009627747MaRDI QIDQ3144366

Renaud Leplaideur, Alexandre Baraviera, Artur Oscar Lopes

Publication date: 7 December 2012

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493712500050

zbMATH Keywords

phase transitionthermodynamic formalismrenormalizationsymbolic dynamicsManneville-Pomeau mapnon-uniformly hyperbolic dynamicsthe shift

Mathematics Subject Classification ID

Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems involving maps of the interval (37E05) Universality and renormalization of dynamical systems (37E20) Renormalization of holomorphic dynamical systems (37F25)

Related Items (10)

About Phase Transition and Zero Temperature ⋮ Renormalization, thermodynamic formalism and quasi-crystals in subshifts ⋮ A general renormalization procedure on the one-dimensional lattice and decay of correlations ⋮ Wild attractors and thermodynamic formalism ⋮ Thermodynamic formalism and \(k\)-Bonacci substitutions ⋮ Phase transitions in one-dimensional translation invariant systems: a Ruelle operator approach ⋮ Sensitive dependence of Gibbs measures at low temperatures ⋮ Flexibility of the pressure function ⋮ The involution kernel and the dual potential for functions in the Walters' family ⋮ An estimation of phase transition ^*

Cites Work

• Renormalisation-induced phase transitions for unimodal maps
• The universal metric properties of nonlinear transformations
• The zeta function, non-differentiability of pressure, and the critical exponent of transition
• Quantitative universality for a class of nonlinear transformations
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• A natural space of functions for the Ruelle operator theorem
• Chaotic period doubling
• Sporadicity: Between periodic and chaotic dynamical behaviors
• ON THERMODYNAMICS OF RATIONAL MAPS. II: NON-RECURRENT MAPS
• Convergence of the Ruelle operator for a function satisfying Bowen’s condition
• Decay of correlations for piecewise smooth maps with indifferent fixed points
• Thermodynamic Formalism
• Local product structure for Equilibrium States
• On an example with a non-analytic topological pressure

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