Computing Garsia entropy for Bernoulli convolutions with algebraic parameters
Hare, Kevin G. ; Kempton, Tom ; Persson, Tomas LU
and Sidorov, Nikita
(2021)
In Nonlinearity
34(7).
p.4744-4763
- Abstract
We introduce a parameter space containing all algebraic integers β ∈ (1, 2] that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution ν β . This allows us to show that dimH(ν β ) = 1 for all β with representations in certain open regions of the parameter space.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/c43d7c17-05a4-42a0-9b36-8645983ae3c1
- author
- Hare, Kevin G.
; Kempton, Tom
; Persson, Tomas
LU
and Sidorov, Nikita
- organization
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- algebraic numbers, Bernoulli convolutions, Hausdorff dimension
- in
- Nonlinearity
- volume
- 34
- issue
- 7
- pages
- 20 pages
- publisher
- London Mathematical Society / IOP Science
- external identifiers
-
- scopus:85110451966
- ISSN
- 0951-7715
- DOI
- 10.1088/1361-6544/abf849
- language
- English
- LU publication?
- yes
- id
- c43d7c17-05a4-42a0-9b36-8645983ae3c1
- date added to LUP
- 2021-09-08 16:39:51
- date last changed
- 2022-04-27 03:47:51
@article{c43d7c17-05a4-42a0-9b36-8645983ae3c1,
abstract = {{<p>We introduce a parameter space containing all algebraic integers β ∈ (1, 2] that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution ν β . This allows us to show that dimH(ν β ) = 1 for all β with representations in certain open regions of the parameter space.</p>}},
author = {{Hare, Kevin G. and Kempton, Tom and Persson, Tomas and Sidorov, Nikita}},
issn = {{0951-7715}},
keywords = {{algebraic numbers; Bernoulli convolutions; Hausdorff dimension}},
language = {{eng}},
number = {{7}},
pages = {{4744--4763}},
publisher = {{London Mathematical Society / IOP Science}},
series = {{Nonlinearity}},
title = {{Computing Garsia entropy for Bernoulli convolutions with algebraic parameters}},
url = {{http://dx.doi.org/10.1088/1361-6544/abf849}},
doi = {{10.1088/1361-6544/abf849}},
volume = {{34}},
year = {{2021}},
}