Integrable geodesic flows on surfaces

Details Integrable geodesic flows on surfaces Integrable geodesic flows on surfaces

2009-05-30

arxiv.org/abs/0906.0100v1

Mathematics

Dynamical Systems

Scientific paper

We propose a new condition $\aleph$ which enables to get new results on integrable geodesic flows on closed surfaces. This paper has two parts. In the first, we strengthen Kozlov's theorem on non-integrability on surfaces of higher genus. In the second, we study integrable geodesic flows on 2-torus. Our main result for 2-torus describes the phase portraits of integrable flows. We prove that they are essentially standard outside, what we call, separatrix chains. The complement to the union of the separatrix chains is $C^0$-foliated by invariant sections of the bundle.

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