Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces

DOI10.1215/00127094-2649425zbMath1328.37033arXiv1111.2060OpenAlexW3098807679MaRDI QIDQ2450926

Steven P. Lalley

Publication date: 23 May 2014

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.2060

zbMATH Keywords

entropygeodesicsLiouville measuresymbolic dynamicsGibbs statenegatively curved surfaceself-intersection counts

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Fundamental group, presentations, free differential calculus (57M05) Symbolic dynamics (37B10) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Flows on surfaces (37E35)

Related Items

Sub-tree counts on hyperbolic random geometric graphs, The variance of closed geodesics in balls and annuli on the modular surface, Intersecting geodesics on the modular surface, Local geometry of random geodesics on negatively curved surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Self-intersections in combinatorial topology: statistical structure
• An analogue of the prime number theorem for closed orbits of Axiom A flows
• Closed geodesics in homology classes on surfaces of variable negative curvature
• Le spectre marqué des longueurs des surfaces à courbure négative. (The spectrum marked by lengths of surfaces with negative curvature)
• Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
• Geodesics with bounded intersection number on surfaces are sparsely distributed
• Canonical perturbation theory of Anosov systems and regularity results for the Livsic cohomology equation
• Distribution of periodic orbits of symbolic and axiom A flows
• The geometry of Teichmüller space via geodesic currents
• Bouts des variétés hyperboliques de dimension 3. (Ends of hyperbolic 3-dimensional manifolds)
• Markov maps associated with Fuchsian groups
• Symbolic dynamics for geodesic flows
• Three remarks on geodesic dynamics and fundamental group
• The central limit theorem for geodesic flows on \(n\)-dimensional manifolds of negative curvature
• Growth of the number of simple closed geodesics on hyperbolic surfaces
• On a theorem of Anosov
• Applications of ergodic theory to the investigation of manifolds of negative curvature
• Expansive one-parameter flows
• Markov partitions for Anosov flows on \(n\)-dimensional manifolds
• A simpler proof of Mirzakhani's simple curve asymptotics
• On U-statistics and v. mise? statistics for weakly dependent processes
• Geodesic flows, interval maps, and symbolic dynamics
• An Algorithm for Simple Curves on Surfaces
• Symbolic Dynamics for Hyperbolic Flows
• The Existence of Probability Measures with Given Marginals
• Distances of Probability Measures and Random Variables
• The Equidistribution of Closed Geodesics
• Angular self-intersections for closed geodesics on surfaces
• A Class of Statistics with Asymptotically Normal Distribution
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms