2009/05/30 by Misha Bialy, Bialy, Misha
Mathematics · #37J35 #37J50 #53D25 #70H07 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.0906.0100
openalex publication_date 2009/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new condition ℵ 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 C0-foliated by invariant sections of the bundle.