A connecting theorem for geodesic flows on the 2-torus

preprint2021arXivOpen access

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 $ST^2$ of the 2-torus in regions without invariant tori.

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A connecting theorem for geodesic flows on the 2-torus

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