Absolute continuity of complex Bernoulli convolutions-Reference-Cited by-同舟云学术

Absolute continuity of complex Bernoulli convolutions

Published:2016-05-16 Issue:3 Volume:161 Page:435-453
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

SHMERKIN PABLO,SOLOMYAK BORIS

Abstract

AbstractWe prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference24 articles.

1. Smoothness of projections, Bernoulli convolutions and the dimension of exceptions;Peres;Duke Math. J.,2000

2. On the `Mandelbrot set' for a pair of linear maps and complex Bernoulli convolutions

3. Properties of measures supported on fat Sierpinski carpets

4. On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions

5. D. Calegary , S. Koch and A. Walker Roots, Schottky semigroups, and a proof of Bandt's conjecture. Preprint. arXiv:1410.8542.

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Fourier decay behavior of homogeneous self-similar measures on the complex plane;Journal of Fractal Geometry;2023-08-01

2. Fourier decay for homogeneous self-affine measures;Journal of Fractal Geometry;2022-07-27

3. Fourier decay for self-similar measures;Proceedings of the American Mathematical Society;2021-05-10

4. Entropy of Bernoulli convolutions and uniform exponential growth for linear groups;Journal d'Analyse Mathématique;2020-03

5. On self-similar measures with absolutely continuous projections and dimension conservation in each direction;Ergodic Theory and Dynamical Systems;2019-06-26