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 language | English |
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Pages (from-to) | 101-130 |
Number of pages | 30 |
Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
Volume | 149 |
Issue number | 1 |
DOIs | |
State | Published - 1 Feb 2019 |
Externally published | Yes |
Keywords
- Young towers
- coupling
- decay of correlations
- explicit rates
- mixing
All Science Journal Classification (ASJC) codes
- General Mathematics