Fourier transforms of Gibbs measures for the Gauss map

DOI10.1007/s00208-015-1241-9zbMath1343.42006arXiv1312.3619OpenAlexW1568654974MaRDI QIDQ261415

F. Blanchet-Sadri, M. Dambrine

Publication date: 23 March 2016

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

Full work available at URL: https://arxiv.org/abs/1312.3619

zbMATH Keywords

Fourier transformHausdorff dimensionGauss maplarge deviationsGibbs measures

Mathematics Subject Classification ID

Large deviations (60F10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Metric theory of continued fractions (11K50) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (34)

Trigonometric series and self-similar sets ⋮ Large sets without Fourier restriction theorems ⋮ Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images ⋮ Decrease of Fourier coefficients of stationary measures ⋮ Characterization of random variables with stationary digits ⋮ Mini-workshop: Differentiable ergodic theory, dimension theory and stable foliations. Abstracts from the mini-workshop held September 28 -- October 4, 2014. ⋮ Attractors of dual continued fractions ⋮ Fourier decay for homogeneous self-affine measures ⋮ Fourier dimension and spectral gaps for hyperbolic surfaces ⋮ Minkowski's question mark measure ⋮ On Minkowski type question mark functions associated with even or odd continued fractions ⋮ Billiards on Pythagorean triples and their Minkowski functions ⋮ Equidistribution for measures defined by digit restrictions ⋮ On the Fourier analytic structure of the Brownian graph ⋮ On the Fourier dimension and a modification ⋮ Hausdorff dimensions for graph-directed measures driven by infinite rooted trees ⋮ FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS ⋮ On oscillatory integrals with Hölder phases ⋮ Exponential mixing of geodesic flows for geometrically finite hyperbolic manifolds with cusps ⋮ Julia sets of hyperbolic rational maps have positive Fourier dimension ⋮ Fourier transform of self-affine measures ⋮ Some results for conjugate equations ⋮ On the Fourier transform of coin-tossing type measures ⋮ On the Fourier-Stieltjes coefficients of the function inverse to the Minkowski function ⋮ Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay ⋮ On the affirmative solution to Salem's problem ⋮ Random walks in the hyperbolic plane and the Minkowski question mark function ⋮ Regularity of Minkowski's question mark measure, its inverse and a class of IFS invariant measures ⋮ Pointwise normality and Fourier decay for self-conformal measures ⋮ An introduction to fractal uncertainty principle ⋮ Fourier decay for self-similar measures ⋮ Explicit Salem sets and applications to metrical Diophantine approximation ⋮ Hausdorff and Fourier dimension of graph of continuous additive processes ⋮ On normal numbers and self-similar measures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Minkowski ?\((x)\) function and Salem's problem
• Equidistribution from fractal measures
• Fractal analysis for sets of non-differentiability of Minkowski's question mark function
• \(M\)-sets and measures
• Seventy years of Rajchman measures
• On a theorem of Kaufman: Cantor-type construction of linear fractal Salem sets
• Hausdorff dimension, projections, and the Fourier transform
• Fourier analysis of continued fractions with restricted quotients
• Perron-Frobenius operators and the Klein-Gordon equation
• Large deviations for countable to one Markov systems
• On Weyl's criterion for uniform distribution
• Large Deviations in Dynamical Systems and Stochastic Processes
• Entropy and large deviation
• Note on a Singular Function of Minkowski
• Metric Number Theory and the Large Sieve
• Continued fractions and Fourier transforms
• On the theorem of Jarník and Besicovitch
• Invariant Measures and Equilibrium States for Some Mappings which Expand Distances
• Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval
• Liouville numbers, Rajchman measures, and small Cantor sets
• Existence of Gibbs measures for countable Markov shifts
• Some Large Deviation Results for Dynamical Systems
• On Some Singular Monotonic Functions Which Are Strictly Increasing
• Probability
• On a problem in simultaneous Diophantine approximation: Littlewood's conjecture
• Phase transitions for countable Markov shifts
• A dimension gap for continued fractions with independent digits

This page was built for publication: Fourier transforms of Gibbs measures for the Gauss map