On transfer operators and maps with random holes. (6th February 2015)

• Record Type: Journal Article
• Authors: Bahsoun, Wael; Schmeling, Jörg; Vaienti, Sandro
• Is Part Of: Nonlinearity. Volume 28:Number 3(2015:Mar.)
• Page Start: 713
• Page End: 727
• Publication Date: 2015-02-06
• Subjects: Transfer operators -- Escape rates -- Hausdorff dimension; 37A05 -- 37E05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/3/713
• Languages: English
• ISSNs: 0951-7715

Abstract

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.