TL;DR
This paper proves that equicontinuous geodesic flows on surfaces and 3-manifolds are necessarily periodic, using recurrence of the return map as a key argument.
Contribution
It establishes the periodicity of equicontinuous geodesic flows on surfaces and extends the result to 3-manifolds, providing new insights into their dynamical behavior.
Findings
Equicontinuous geodesic flows on surfaces are periodic.
Similar periodicity result holds for flows on 3-manifolds.
Return map recurrence implies flow periodicity.
Abstract
The author shows that equicontinuous geodesic flows on surfaces are periodic. A similar result for flows on 3-manifolds is also proven. The idea of the proof is to show that the return map is recurrent and therefore periodic.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows