Equilibrium state for one-dimensional Lorenz-like expanding maps

DOI10.1007/s00574-018-0084-xzbMath1409.37047OpenAlexW2595237822WikidataQ129968716 ScholiaQ129968716MaRDI QIDQ1757111

M. A. Bronzi, Juliano G. Oler

Publication date: 2 January 2019

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-018-0084-x

zbMATH Keywords

Lorenz mapsequilibrium state

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems involving maps of the interval (37E05)

Related Items

Phase transitions for one-dimensional Lorenz-like expanding maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
• Structural stability of Lorenz attractors
• The structure of Lorenz attractors
• A function with countably many ergodic equilibrium states
• The Lorenz equations: bifurcations, chaos, and strange attractors
• A characterization of hyperbolic potentials of rational maps
• Equilibrium states of weakly hyperbolic one-dimensional maps for Hölder potentials
• Equilibrium states of interval maps for hyperbolic potentials
• Large deviations for systems with non-uniform structure
• On the uniqueness of equilibrium states for piecewise monotone mappings
• On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions
• Topological conjugation of Lorenz maps by β-transformations
• A point is normal for almost all maps βx+α mod 1 or generalized β-transformations
• Generalized bounded variation and applications to piecewise monotonic transformations
• The Maximal Measure for Linear Mod One Transformations
• Equilibrium states for piecewise monotonic transformations
• Examples for the Nonuniqueness of the Equilibrium State
• The topological classification of Lorenz attractors
• The Real Fatou Conjecture
• Convergence of the transfer operator for rational maps
• Equilibrium States and Hausdorff Measures for Interval Maps
• Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps
• Deterministic Nonperiodic Flow
• On the transfer operator for rational functions on the Riemann sphere
• Equilibrium states beyond specification and the Bowen property
• Symbolic Dynamics and Transformations of the Unit Interval
• ENTROPY OF EQUILIBRIUM MEASURES OF CONTINUOUS PIECEWISE MONOTONIC MAPS
• Ergodic theory of equilibrium states for rational maps
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms