Bernoulli convolutions and 1D dynamics
Kempton, Tom and Persson, Tomas LU
(2015)
In Nonlinearity
28(11).
p.3921-3934
- Abstract
- We describe a family phi(lambda) of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems phi(lambda) and give some numerical evidence to suggest values of lambda for which phi(lambda) may be piecewise convex.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8548680
- author
- Kempton, Tom
and Persson, Tomas
LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- bernoulli convolutions, tent maps, absolutely continuous invariant, measures
- in
- Nonlinearity
- volume
- 28
- issue
- 11
- pages
- 3921 - 3934
- publisher
- London Mathematical Society / IOP Science
- external identifiers
-
- wos:000366670600010
- scopus:84947559445
- ISSN
- 0951-7715
- DOI
- 10.1088/0951-7715/28/11/3921
- language
- English
- LU publication?
- yes
- id
- c7376e8f-9434-41f6-b4d1-f65733e6de74 (old id 8548680)
- alternative location
- https://arxiv.org/abs/1501.06740
- date added to LUP
- 2016-04-01 09:52:51
- date last changed
- 2022-04-27 08:24:24
@article{c7376e8f-9434-41f6-b4d1-f65733e6de74,
abstract = {{We describe a family phi(lambda) of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems phi(lambda) and give some numerical evidence to suggest values of lambda for which phi(lambda) may be piecewise convex.}},
author = {{Kempton, Tom and Persson, Tomas}},
issn = {{0951-7715}},
keywords = {{bernoulli convolutions; tent maps; absolutely continuous invariant; measures}},
language = {{eng}},
number = {{11}},
pages = {{3921--3934}},
publisher = {{London Mathematical Society / IOP Science}},
series = {{Nonlinearity}},
title = {{Bernoulli convolutions and 1D dynamics}},
url = {{http://dx.doi.org/10.1088/0951-7715/28/11/3921}},
doi = {{10.1088/0951-7715/28/11/3921}},
volume = {{28}},
year = {{2015}},
}