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On transfer operators and maps with random holes

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journal contribution
posted on 2016-05-25, 13:51 authored by Wael BahsounWael Bahsoun, Jorg Schmeling, Sandro Vaienti
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

NONLINEARITY

Volume

28

Issue

3

Pages

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 Society

Version

  • 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

2015

Notes

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

0951-7715

Language

  • en