Beyond Bowen’s Specification Property

DOI10.1007/978-3-030-74863-0_1zbMath1485.37029arXiv2009.09256OpenAlexW3087113524MaRDI QIDQ5016434

Vaughn Climenhaga, Daniel J. Thompson

Publication date: 13 December 2021

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.09256

zbMATH Keywords

thermodynamic formalismuniformly hyperbolic systemsHölder continuous potentialunique equilibrium state

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Invariant manifold theory for dynamical systems (37D10)

Related Items

Multifractal analysis of measures arising from random substitutions ⋮ Decay of correlations for some non-uniformly hyperbolic attractors ⋮ Entropy spectrum of rotation classes

Cites Work

• Geodesic Flows Modelled by Expansive Flows
• Equilibrium states in dynamical systems via geometric measure theory
• On the topological entropy of saturated sets
• Intrinsic Markov Chains
• On controlled specification and uniqueness of the equilibrium state in expansive systems
• ENTROPY, A COMPLETE METRIC INVARIANT FOR AUTOMORPHISMS OF THE TORUS
• Similarity of automorphisms of the torus
• Periodic Points and Measures for Axiom a Diffeomorphisms
• Entropy-Expansive Maps
• Periodic Orbits for Hyperbolic Flows
• SRB measures as zero-noise limits
• Some Large Deviation Results for Dynamical Systems
• \(\beta\)-shifts have unique maximal measure
• Equilibrium states for \(\beta\)-transformations and related transformations
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Phase transitions for countable Markov shifts
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ergodic properties of equilibrium measures for smooth three dimensional flows
• On intrinsic ergodicity and weakenings of the specification property
• A non-dynamically coherent example on \(\mathbb T^3\)
• Unique equilibrium states for flows and homeomorphisms with non-uniform structure
• Topological features of flows with the reparametrized gluing orbit property
• Non-uniform specification and large deviations for weak Gibbs measures
• Zero-entropy dynamical systems with the gluing orbit property
• Nonpositively curved manifolds of higher rank
• On surfaces with no conjugate points
• On topological Tits buildings and their classification
• Manifolds of nonpositive curvature and their buildings
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Axial isometries of manifolds of non-positive curvature
• Maps of intervals with indifferent fixed points: thermodynamic formalism and phase transitions
• Ergodic theory on compact spaces
• Contributions to the stability conjecture
• The uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds
• What are SRB measures, and which dynamical systems have them?
• Hölder regularity of horocycle foliations.
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• On the mixing property for hyperbolic systems
• S-limited shifts
• Unique equilibrium states for geodesic flows in nonpositive curvature
• \(\beta\)-expansions and symbolic dynamics
• Subshifts of finite type and sofic systems
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Intrinsic ergodicity beyond specification: \({\beta}\)-shifts, \(S\)-gap shifts, and their factors
• SRB measures for partially hyperbolic systems whose central direction is mostly contracting
• Specification and towers in shift spaces
• Hyperbolic flows
• The weak specification property for geodesic flows on \(\mathrm{CAT}(-1)\) spaces
• Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points
• Properties of equilibrium states for geodesic flows over manifolds without focal points
• The unique measure of maximal entropy for a compact rank one locally CAT(0) space
• Strong symbolic dynamics for geodesic flows on \(\operatorname{CAT}(-1)\) spaces and other metric Anosov flows
• On the Patterson-Sullivan measure for geodesic flows on rank 1 manifolds without focal points
• Denseness of intermediate pressures for systems with the Climenhaga-Thompson structures
• Positive entropy equilibrium states
• Building thermodynamics for non-uniformly hyperbolic maps
• Entropic stability beyond partial hyperbolicity
• Expansive one-parameter flows
• Geodesic flows are Bernoullian
• Partial hyperbolicity and specification
• Ergodic universality of some topological dynamical systems
• A panorama of specification-like properties and their consequences
• Pressures for geodesic flows of rank one manifolds
• Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems
• Intrinsic ergodicity of partially hyperbolic diffeomorphisms with a hyperbolic linear part
• Maximizing measures for partially hyperbolic systems with compact center leaves
• Intrinsic ergodicity via obstruction entropies
• Large deviations for systems with non-uniform structure
• Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• A sufficient condition for robustly minimal foliations
• Unique equilibrium states for some intermediate beta transformations
• Foundations of Ergodic Theory
• Equilibrium states in negative curvature
• Fluctuations of Observables in Dynamical Systems: From Limit Theorems to Concentration Inequalities
• On the weaker forms of the specification property and their applications
• Some systems with unique equilibrium states
• Maximizing entropy for a hyperbolic flow
• Flows with Unique Equilibrium States
• On the Bernoulli nature of systems with some hyperbolic structure
• Symbolic dynamics for $\beta$-shifts and self-normal numbers
• On the variational principle for the topological entropy of certain non-compact sets
• Unique equilibrium states for Bonatti–Viana diffeomorphisms
• Introduction to Riemannian Manifolds
• Equilibrium states for partially hyperbolic diffeomorphisms with hyperbolic linear part
• Large deviations estimates for dynamical systems without the specification property. Application to the β-shifts
• On the Variety of Manifolds without Conjugate Points
• Ergodicité et équidistribution en courbure négative
• Nonuniformly hyperbolic K-systems are Bernoulli
• Equilibrium states beyond specification and the Bowen property
• SRB measures for non-hyperbolic systems with multidimensional expansion
• Unique equilibrium states, large deviations and Lyapunov spectra for the Katok map
• Open problems and questions about geodesics
• Equilibrium states for certain partially hyperbolic attractors
• An Introduction to the Kolmogorov–Bernoulli Equivalence
• Intrinsic ergodicity for factors of $(-\beta)$ -shifts
• Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees
• Equilibrium states for Mañé diffeomorphisms
• One-sided almost specification and intrinsic ergodicity