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On transfer operators and maps with random holes

Bahsoun, Wael; Schmeling, Jörg LU and Vaienti, Sandro (2015) In Nonlinearity 28(3). p.713-727
Abstract
We study Markov interval maps with random holes. The holes are not necessarily elements of the Markov partition. Under a suitable, and physically relevant, assumption on the noise, we show that the transfer operator associated with the random open system can be reduced to a transfer operator associated with the closed deterministic system. Exploiting this fact, we show that the random open system admits a unique (meaningful) absolutely continuous conditionally stationary measure. Moreover, we prove the existence of a unique probability equilibrium measure supported on the survival set, and we study its Hausdorff dimension.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Transfer operators, Escape rates, Hausdorff dimension
in
Nonlinearity
volume
28
issue
3
pages
713 - 727
publisher
London Mathematical Society / IOP Science
external identifiers
  • wos:000350568700011
  • scopus:84923802220
ISSN
0951-7715
DOI
10.1088/0951-7715/28/3/713
language
English
LU publication?
yes
id
36eb0337-7af0-448d-b336-3379d97674f2 (old id 5297220)
date added to LUP
2015-04-24 12:49:00
date last changed
2017-03-16 14:24:00
@article{36eb0337-7af0-448d-b336-3379d97674f2,
  abstract     = {We study Markov interval maps with random holes. The holes are not necessarily elements of the Markov partition. Under a suitable, and physically relevant, assumption on the noise, we show that the transfer operator associated with the random open system can be reduced to a transfer operator associated with the closed deterministic system. Exploiting this fact, we show that the random open system admits a unique (meaningful) absolutely continuous conditionally stationary measure. Moreover, we prove the existence of a unique probability equilibrium measure supported on the survival set, and we study its Hausdorff dimension.},
  author       = {Bahsoun, Wael and Schmeling, Jörg and Vaienti, Sandro},
  issn         = {0951-7715},
  keyword      = {Transfer operators,Escape rates,Hausdorff dimension},
  language     = {eng},
  number       = {3},
  pages        = {713--727},
  publisher    = {London Mathematical Society / IOP Science},
  series       = {Nonlinearity},
  title        = {On transfer operators and maps with random holes},
  url          = {http://dx.doi.org/10.1088/0951-7715/28/3/713},
  volume       = {28},
  year         = {2015},
}