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Integrable Geodesic Flows on Surfaces

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Abstract

We propose a new condition \({{\aleph}}\) which enables us 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 a 2-torus. Our main result for a 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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  1. Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel aviv, Israel

    Misha Bialy

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  1. Misha Bialy
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Correspondence to Misha Bialy.

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Bialy, M. Integrable Geodesic Flows on Surfaces. Geom. Funct. Anal. 20, 357–367 (2010). https://doi.org/10.1007/s00039-010-0069-4

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  • DOI: https://doi.org/10.1007/s00039-010-0069-4

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