A connecting theorem for geodesic flows on the 2-torus
Stefan Klempnauer
TL;DR
This paper proves the existence of connecting geodesics on the 2-torus's tangent bundle in regions lacking invariant tori, using Mather's result on twist maps to advance understanding of geodesic flow dynamics.
Contribution
It introduces a connecting theorem for geodesic flows on the 2-torus, extending the application of Mather's twist map results to geometric dynamical systems.
Findings
Existence of connecting geodesics in certain regions of the 2-torus
Application of Mather's theorem to geodesic flows
Regions without invariant tori are characterized by connecting orbits
Abstract
We use a result of J. Mather on the existence of connecting orbits for compositions of monotone twist maps of the cylinder to prove the existence of connecting geodesics on the unit tangent bundle of the 2-torus in regions without invariant tori.
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Taxonomy
TopicsGeometry and complex manifolds · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows