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Diversified homotopic behavior of closed orbits of some $\mathbb{R}$-covered Anosov flows

Published online by Cambridge University Press:  10 November 2014

SÉRGIO R. FENLEY
SÉRGIO R. FENLEY*
Affiliation:
Florida State University, Tallahassee, FL 32306-4510, USA email fenley@math.fsu.edu
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Abstract

We produce infinitely many examples of Anosov flows in closed $3$-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of the flow. In the other subset every closed orbit is freely homotopic to only one other closed orbit. The examples are obtained by Dehn surgery on geodesic flows. The manifolds are toroidal and have Seifert pieces and atoroidal pieces in their torus decompositions.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 767 - 780
Copyright
© Cambridge University Press, 2014 

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