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Transactions of the American Mathematical Society

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Local and global properties of limit sets of foliations of quasigeodesic Anosov flows

Author: Sérgio R. Fenley
Journal: Trans. Amer. Math. Soc. 350 (1998), 3923-3941
MSC (1991): Primary 57R30, 58F25, 58F15; Secondary 58F22, 53C12
MathSciNet review: 1432199
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Abstract: A nonsingular flow is quasigeodesic when all flow lines are efficient in measuring distances in relative homotopy classes. We analyze the quasigeodesic property for Anosov flows in $3$-manifolds which have negatively curved fundamental group. We show that this property implies that limit sets of stable and unstable leaves (in the universal cover) vary continuously in the sphere at infinity. It also follows that the union of the limit sets of all stable (or unstable) leaves is not the whole sphere at infinity. Finally, under the quasigeodesic hypothesis we completely determine when limit sets of leaves in the universal cover can intersect. This is done by determining exactly when flow lines in the universal cover share an ideal point.

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Sérgio R. Fenley
Affiliation: Department of Mathematics, Washington University, St. Louis, Missouri 63130; Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000

Received by editor(s): December 18, 1995
Received by editor(s) in revised form: November 11, 1996
Additional Notes: Reseach supported by NSF grants DMS-9201744 and an NSF postdoctoral fellowship
Article copyright: © Copyright 1998 American Mathematical Society