Geodesic flows on negatively curved manifolds. II
Author:
Patrick Eberlein
Journal:
Trans. Amer. Math. Soc. 178 (1973), 57-82
MSC:
Primary 58F10; Secondary 53C20, 53C70
DOI:
https://doi.org/10.1090/S0002-9947-1973-0314084-0
MathSciNet review:
0314084
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Abstract | References | Similar Articles | Additional Information
Abstract: Let M be a complete Riemannian manifold with sectional curvature , SM the unit tangent bundle of M,
the geodesic flow on SM and
the set of nonwandering points relative to
.
is topologically mixing (respectively topologically transitive) on SM if for any open sets 0, U of SM there exists
such that
implies
(respectively there exists
such that
). For each vector
we define stable and unstable sets
and
, and we relate topological mixing (respectively topological transitivity) of
to the existence of a vector
such that
(respectively
) is dense in SM. If M is a Visibility manifold (implied by
) and if
then
is topologically mixing on SM. Let
{Visibility manifolds M of dimension n such that
is topologically mixing on SM}. For each
,
is closed under normal (Galois) Riemannian coverings. If
we classify {
is dense in SM}, and M is compact if and only if this set = SM. We also consider the case where
is a proper subset of SM.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1973-0314084-0
Keywords:
Geodesic flow,
prolongational limit sets,
nonwandering points,
stable and unstable sets,
topological transitivity,
topological mixing,
Axiom 1,
Visibility manifold
Article copyright:
© Copyright 1973
American Mathematical Society