Counterexamples in non-positive curvature

Yves Coudène; Barbara Schapira

doi:10.3934/dcds.2011.30.1095

Article Contents

2011, Volume 30, Issue 4: 1095-1106. Doi: 10.3934/dcds.2011.30.1095

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Counterexamples in non-positive curvature

Yves Coudène^1, and
Barbara Schapira^2,

1.
Université de Bretagne Occidentale, 6 av. Le Gorgeu, 29238 Brest cedex
2.
LAMFA, Université Picardie Jules Verne, 33 rue St Leu 80000 Amiens

Received: March 31, 2010

Revised: July 31, 2010

Published: September 2011

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Abstract

We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface are not dense in the set of probability measures invariant by the geodesic flow. Finally, we give examples of complete rank one surfaces for which the non wandering set of the geodesic flow is connected, the periodic orbits are dense in that set, yet the geodesic flow is not transitive in restriction to its non wandering set.

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Mathematics Subject Classification: Primary: 37B10, 37C40; Secondary: 34C28.

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References

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