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On transfer operators and maps with random holes
journal contribution
posted on 2016-05-25, 13:51 authored by Wael BahsounWael Bahsoun, Jorg Schmeling, Sandro VaientiWe 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.
History
School
- Science
Department
- Mathematical Sciences
Published in
NONLINEARITYVolume
28Issue
3Pages
713 - 727 (15)Citation
BAHSOUN, W., SCHMELING, J. and VAIENTI, S., 2015. On transfer operators and maps with random holes. Nonlinearity, 28 (3), pp. 713 - 727.Publisher
© IOP Publishing Ltd & London Mathematical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2015Notes
This article was published in the journal Nonlinearity and the definitive version is available at: http://iopscience.iop.org/0951-7715/28/3/713)ISSN
0951-7715Publisher version
Language
- en