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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
; and
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
IOP Publishing
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
2016-04-01 10:41:59
date last changed
2025-10-14 11:27:24
@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}},
  keywords     = {{Transfer operators; Escape rates; Hausdorff dimension}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{713--727}},
  publisher    = {{IOP Publishing}},
  series       = {{Nonlinearity}},
  title        = {{On transfer operators and maps with random holes}},
  url          = {{http://dx.doi.org/10.1088/0951-7715/28/3/713}},
  doi          = {{10.1088/0951-7715/28/3/713}},
  volume       = {{28}},
  year         = {{2015}},
}