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On transfer operators and maps with random holes

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Author

Summary, in English

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.

Department/s

Publishing year

2015

Language

English

Pages

713-727

Publication/Series

Nonlinearity

Volume

28

Issue

3

Document type

Journal article

Publisher

London Mathematical Society / IOP Science

Topic

  • Mathematics

Keywords

  • Transfer operators
  • Escape rates
  • Hausdorff dimension

Status

Published

Research group

  • Dynamical systems

ISBN/ISSN/Other

  • ISSN: 0951-7715