Local limit theorems for suspended semiflows

Jon Aaronson; Dalia Terhesiu

doi:10.3934/dcds.2020294

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2020, Volume 40, Issue 12: 6575-6609. Doi: 10.3934/dcds.2020294

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Local limit theorems for suspended semiflows

Jon Aaronson^1, , and
Dalia Terhesiu^2, ,

1.
School of Math. Sciences, Tel Aviv University, 69978 Tel Aviv, Israel, Webpage: http://www.math.tau.ac.il/~aro
2.
Department of Mathematics, University of Exeter, Exeter EX4 4QF, UK

Dedicated to the memory of Nat Friedman

Received: May 31, 2019

Revised: June 30, 2020

Early access: August 2020

Published: August 2020

Aaronson's research was partially supported by ISF grant No. 1289/17

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Abstract

We prove local limit theorems for a cocycle over a semiflow by establishing topological, mixing properties of the associated skew product semiflow. We also establish conditional rational weak mixing of certain skew product semiflows and various mixing properties including order 2 rational weak mixing of hyperbolic geodesic flows on the tangent spaces of cyclic covers.

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Mathematics Subject Classification: Primary: 37A40, 60F05.

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