Distribution of the periodic points of the Farey map

DOI10.1007/s00220-019-03283-0zbMath1465.37046arXiv1704.08971OpenAlexW2963306700MaRDI QIDQ1729881

Byron Heersink

Publication date: 28 February 2019

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.08971

zbMATH Keywords

geodesic flowcross sectionmodular surfaceFarey map

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Relations between ergodic theory and number theory (37A44)

Related Items (4)

Asymptotic Counting in Conformal Dynamical Systems ⋮ Distribution of periodic points of certain Gauss shifts with infinite invariant measure ⋮ Distribution of the reduced quadratic irrationals arising from the odd continued fraction expansion ⋮ Geodesic flows and the mother of all continued fractions

Cites Work

• Unnamed Item
• The asymptotic distribution of circles in the orbits of Kleinian groups
• An analogue of the prime number theorem for closed orbits of Axiom A flows
• Algorithms with mediant convergents and their metrical theory
• Fractal analysis for sets of non-differentiability of Minkowski's question mark function
• Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps
• The coding for geodesic flows on a modular surface
• Local limit theorem and distribution of periodic orbits of Lasota-Yorke transformations with infinite Markov partition
• Metrical theory for Farey continued fractions
• Perturbation theory for linear operators.
• Quadratic irrationals and linking numbers of modular knots
• Presentation functions, fixed points, and a theory of scaling function dynamics.
• Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals
• Counting visible circles on the sphere and Kleinian groups
• Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
• Distribution of closed geodesics on the modular surface and quadratic irrationals
• La théorie de Fredholm
• The Modular Surface and Continued Fractions
• Asymptotic Counting in Conformal Dynamical Systems
• Bowen's equidistribution theory and the Dirichlet density theorem
• Distribution of Lévy constants for quadratic numbers
• On a $\zeta$ function related to the continued fraction transformation
• Proof of the Quasi-Ergodic Hypothesis
• On the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces
• Tauberian Theory
• Equidistribution and counting for orbits of geometrically finite hyperbolic groups
• Products of matrices and and the distribution of reduced quadratic irrationals
• Produits tensoriels topologiques et espaces nucléaires
• On asymptotic properties of a number theoretic function arising out of a spin chain model in statistical mechanics

This page was built for publication: Distribution of the periodic points of the Farey map