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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.
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author
organization
publishing date
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)
date added to LUP
2016-01-29 10:56:16
date last changed
2017-03-14 13:40:52
@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},
  keyword      = {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},
  volume       = {28},
  year         = {2015},
}