Asymptotic Counting in Conformal Dynamical Systems

DOI10.1090/memo/1327zbMath1482.37002arXiv1704.06896OpenAlexW3185044041MaRDI QIDQ3380559

Mark Pollicott, Mariusz Urbański

Publication date: 29 September 2021

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.06896

zbMATH Keywords

Poincaré seriesconformal dynamicsasymptotic counting functions

Mathematics Subject Classification ID

Asymptotic results on counting functions for algebraic and topological structures (11N45) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Symbolic dynamics (37B10) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Dynamical systems involving maps of trees and graphs (37E25) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Relations between ergodic theory and number theory (37A44)

Related Items (7)

Porosity in Conformal Dynamical Systems ⋮ Hyperbolic systems, zeta functions and other friends ⋮ The dimension spectrum of conformal graph directed Markov systems ⋮ Level-2 large deviation principle for countable Markov shifts without Gibbs states ⋮ Julia sets of hyperbolic rational maps have positive Fourier dimension ⋮ Distribution of the periodic points of the Farey map ⋮ Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations

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