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Hyperbolic geometry and pointwise ergodic theorems

Published online by Cambridge University Press:  12 December 2017

LEWIS BOWEN  and
AMOS NEVO
LEWIS BOWEN
Affiliation:
Mathematics Department, 1 University Station C1200, University of Texas at Austin, Austin, TX 78712, USA email lpbowen@math.utexas.edu
AMOS NEVO
Affiliation:
Mathematics Department, Technion – Israel Institute of Technology, Haifa 32000, Israel email anevo@tx.technion.ac.il
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Abstract

We establish pointwise ergodic theorems for a large class of natural averages on simple Lie groups of real rank one, going well beyond the radial case considered previously. The proof is based on a new approach to pointwise ergodic theorems, which is independent of spectral theory. Instead, the main new ingredient is the use of direct geometric arguments in hyperbolic space.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 10 , October 2019 , pp. 2689 - 2716
Copyright
© Cambridge University Press, 2017 

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