Explicit coupling argument for non-uniformly hyperbolic transformations. Issue 1 (6th July 2018)

• Record Type: Journal Article
• Authors: Korepanov, A.; Kosloff, Z.; Melbourne, I.
• Is Part Of: Proceedings. Volume 149:Issue 1(2019)
• Page Start: 101
• Page End: 130
• Publication Date: 2018-07-06
• Subjects: coupling, -- mixing, -- decay of correlations, -- Young towers, -- explicit rates; Primary 37A25, -- Secondary 37D25; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210518000161
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : The transfer operator corresponding to a uniformly expanding map enjoys good spectral properties. We verify that coupling yields explicit estimates that depend continuously on the expansion and distortion constants of the map. For non-uniformly expanding maps with a uniformly expanding induced map, we obtain explicit estimates for mixing rates (exponential, stretched exponential, polynomial) that again depend continuously on the constants for the induced map together with data associated with the inducing time. Finally, for non-uniformly hyperbolic transformations, we obtain the corresponding estimates for rates of decay of correlations.