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On the geodesic flow on CAT(0) spaces

Part of: Low-dimensional topology Ergodic theory

Published online by Cambridge University Press:  15 August 2019

CHARALAMPOS CHARITOS ,
IOANNIS PAPADOPERAKIS  and
GEORGIOS TSAPOGAS
CHARALAMPOS CHARITOS
Affiliation:
Mathematics Laboratory, Agricultural University of Athens, 11855Athens, Greece email [email protected], [email protected], [email protected]
IOANNIS PAPADOPERAKIS
Affiliation:
Mathematics Laboratory, Agricultural University of Athens, 11855Athens, Greece email [email protected], [email protected], [email protected]
GEORGIOS TSAPOGAS
Affiliation:
Mathematics Laboratory, Agricultural University of Athens, 11855Athens, Greece email [email protected], [email protected], [email protected]
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Abstract

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.

Keywords

geodesic flowmixingCAT(0) spacetopological dynamics

MSC classification

Primary: 37A25: Ergodicity, mixing, rates of mixing
Secondary: 57M50: Geometric structures on low-dimensional manifolds
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 12 , December 2020 , pp. 3310 - 3338
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Copyright
© Cambridge University Press, 2019

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