On transfer operators and maps with random holes

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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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Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Transfer operators, Escape rates, Hausdorff dimension
Original languageEnglish
Pages (from-to)713-727
JournalNonlinearity
Volume28
Issue number3
Publication statusPublished - 2015
Publication categoryResearch
Peer-reviewedYes