Livsic theorems, maximizing measures and the stable norm

DOI10.1080/14689360410001658990zbMath1057.37023OpenAlexW1978754539MaRDI QIDQ4470310

Mark Pollicott, Richard Sharp

Publication date: 22 June 2004

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689360410001658990

zbMATH Keywords

hyperbolic systemmaximizing measuresvalues around closed orbits

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Dynamical systems with hyperbolic orbits and sets (37D05) Symbolic dynamics (37B10) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20)

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Stable topological transitivity properties of ℝⁿ-extensions of hyperbolic transformations ⋮ Ergodic optimization for some dynamical systems beyond uniform hyperbolicity ⋮ Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows* ⋮ Entropy production in Gaussian thermostats ⋮ Lipschitz sub-actions for locally maximal hyperbolic sets of a \(C^1\) map ⋮ Ergodic optimization for hyperbolic flows and Lorenz attractors ⋮ Entropy and maximizing measures of generic continuous functions ⋮ Sturmian maximizing measures for the piecewise-linear cosine family ⋮ A LARGE DEVIATION PRINCIPLE FOR THE EQUILIBRIUM STATES OF HÖLDER POTENTIALS: THE ZERO TEMPERATURE CASE ⋮ Functions for relative maximization ⋮ Ergodic optimization in dynamical systems ⋮ The marked length spectrum of Anosov manifolds

Cites Work

• Action minimizing invariant measures for positive definite Lagrangian systems
• Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
• Markov maps associated with Fuchsian groups
• Symbolic dynamics for geodesic flows
• On the cohomology of certain dynamical systems
• Zeta-functions for expanding maps and Anosov flows
• Stable norms of surfaces: local structure of the unit ball at rational directions
• Cohomology classes of dynamically non-negative \(C^ k\) functions.
• Cohomological inequalities for finite topological Markov chains
• Markov partitions for Anosov flows on \(n\)-dimensional manifolds
• La condition de Walters
• Lyapunov minimizing measures for expanding maps of the circle
• Geometrical Markov coding of geodesics on surfaces of constant negative curvature
• Semi-rigidity of horocycle flows over compact surfaces of variable negative curvature
• Symbolic Dynamics for Hyperbolic Flows
• Sub-actions for Anosov flows

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