Quantitative mixing results and inner functions

DOI10.1007/s00208-006-0036-4zbMath1125.30019OpenAlexW2038488033MaRDI QIDQ862375

Domingo Pestana, María V. Melián, José Lúis Fernandez Perez

Publication date: 24 January 2007

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10016/6478

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Ergodicity, mixing, rates of mixing (37A25) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (19)

A central limit theorem for inner functions ⋮ Cheeger isoperimetric constant of Gromov hyperbolic manifolds and graphs ⋮ The shrinking target problem for matrix transformations of tori: revisiting the standard problem ⋮ Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps ⋮ Parabolicity on graphs ⋮ Dichotomy law for shrinking target problems in a nonautonomous dynamical system: Cantor series expansion ⋮ A Survey on the Dimension Theory in Dynamical Diophantine Approximation ⋮ Quantitative recurrence properties for beta-dynamical system ⋮ Quantitative recurrence properties and homogeneous self-similar sets ⋮ Quantitative recurrence properties for self-conformal sets ⋮ The dynamical Borel-Cantelli Lemma and the waiting time problems ⋮ Isoperimetric inequalities in Riemann surfaces and graphs ⋮ A dynamical dimension transference principle for dynamical Diophantine approximation ⋮ A note on isoperimetric inequalities of Gromov hyperbolic manifolds and graphs ⋮ Modified shrinking target problems on self-conformal sets ⋮ Quasi-isometries and isoperimetric inequalities in planar domains ⋮ Quantitative recurrence properties in conformal iterated function systems ⋮ Dynamical Diophantine approximation of beta expansions of formal Laurent series ⋮ Dynamical Borel–Cantelli lemma for recurrence under Lipschitz twists

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pointwise convergence on the boundary in the Denjoy-Wolff theorem
• Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics
• Entropy of inner functions
• Ergodicity of some mappings of the circle and the line
• Quantitative recurrence results
• Capacity distortion by inner functions in the unit ball of \(\mathbb{C}^n\)
• Recurrence, dimensions, and Lyapunov exponents.
• Logarithm laws for flows on homogeneous spaces
• The method of trigonometric sums in the metric theory of diophantine approximations of dependent quantities
• Pointwise dimensions for Poincaré recurrences associated with maps and special flows
• Distortion of boundary sets under inner functions. II
• Dimension via waiting time and recurrence
• On convergence to the Denjoy-Wolff point
• The Bernoulli property of inner functions
• Recurrence and algorithmic information
• Hausdorff dimension of measures via Poincaré recurrence

This page was built for publication: Quantitative mixing results and inner functions