scholarly journals A partial criterion for ergodicity of geodesic flows on surfaces with infinite area and negative curvature

1993 ◽  
Vol 69 (5) ◽  
pp. 115-118
Author(s):  
Hiroshi Shirakawa
Keyword(s):  
Negative Curvature ◽  
Geodesic Flows ◽  
Flows On Surfaces ◽  
Partial Criterion

Expansive geodesic flows on surfaces

1993 ◽  
Vol 13 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Miguel Paternain
Keyword(s):  
Geodesic Flow ◽  
Compact Surface ◽  
Conjugate Points ◽  
Riemannian Surface ◽  
Geodesic Flows ◽  
Flows On Surfaces

AbstractWe prove the following result: if M is a compact Riemannian surface whose geodesic flow is expansive, then M has no conjugate points. This result and the techniques of E. Ghys imply that all expansive geodesic flows of a compact surface are topologically equivalent.

Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows

1989 ◽  
Vol 9 (3) ◽  
pp. 427-432 ◽  
Author(s):  
Renato Feres ◽  
Anatoly Katok
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Riemannian Manifolds ◽  
Negative Curvature ◽  
Geodesic Flows ◽  
Tensor Fields ◽  
Invariant Tensor ◽  
Affine Connections

AbstractWe consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.

Destroying ergodicity in geodesic flows on surfaces

Nonlinearity ◽  
2005 ◽  
Vol 19 (1) ◽  
pp. 149-169 ◽  
Author(s):  
Victor J Donnay
Keyword(s):  
Geodesic Flows ◽  
Flows On Surfaces
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