Explicit coupling argument for non-uniformly hyperbolic transformations

A. Korepanov, Z. Kosloff, I. Melbourne

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

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.

Original languageAmerican English
Pages (from-to)101-130
Number of pages30
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume149
Issue number1
DOIs
StatePublished - 1 Feb 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 Royal Society of Edinburgh.

Keywords

  • Young towers
  • coupling
  • decay of correlations
  • explicit rates
  • mixing

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