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

Fenley, Sérgio

doi:10.1090/S0002-9947-98-01973-4

Local and global properties of limit sets of foliations of quasigeodesic Anosov flows
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by Sérgio R. Fenley PDF

Trans. Amer. Math. Soc. 350 (1998), 3923-3941 Request permission

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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