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arXiv · 1509.09218

Hyperbolic geometry and pointwise ergodic theorems

Lewis Bowen·Amos Nevo
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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.

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Lewis Bowen, Amos Nevo. 2015-09-30. Hyperbolic geometry and pointwise ergodic theorems. https://arxiv.org/abs/1509.09218

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