On the geodesic flow on CAT(0) spaces

On the geodesic flow on CAT(0) spaces

Under certain assumptions on CAT(0) spaces, we show that the geodesic flow is topologically mixing. In particular, the Bowen–Margulis’ measure finiteness assumption used by Ricks [Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces. Ergod. Th. & Dynam...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2020-12, Vol.40 (12), p.3310-3338
Main Authors: CHARITOS, CHARALAMPOS, PAPADOPERAKIS, IOANNIS, TSAPOGAS, GEORGIOS
Format: Article
Language:eng
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Summary:Under certain assumptions on CAT(0) spaces, we show that the geodesic flow is topologically mixing. In particular, the Bowen–Margulis’ measure finiteness assumption used by Ricks [Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces. Ergod. Th. & Dynam. Sys. 37 (2017), 939–970] is removed. We also construct examples of CAT(0) spaces that do not admit finite Bowen–Margulis measure.
ISSN:0143-3857
1469-4417