Abstract
On the unit tangent bundle of a nonflat compact nonpositively curved surface, we prove that there is a unique probability Borel measure invariant by a horocyclic flow which gives full measure to the set of rank 1 vectors recurrent by the geodesic flow. If we assume in addition that the surface has no flat strips, we show that the horocyclic flow is uniquely ergodic. These results are valid for any parametrization of the horocyclic flow.
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Acknowledgment
The author wishes to thank his Ph.D. advisor Yves Coudène for the many helpful suggestions.
Funding
This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 754362.
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Clotet, S.B. Unique ergodicity of horocyclic flows on nonpositively curved surfaces. Isr. J. Math. (2024). https://doi.org/10.1007/s11856-024-2662-5
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DOI: https://doi.org/10.1007/s11856-024-2662-5