Integrable geodesic flow in 3D and webs of maximal rank
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DOI: 10.1007/s13324-024-00987-y
Abstract: We characterize geodesic flows, admitting two commuting quadratic integrals with common principal directions, in terms of the geodesic 4-webs such that the tangents to the web leaves are common zero directions of the integrals. We… read more here.
Keywords: geodesic flow; webs maximal; integrable geodesic; maximal rank ... See more keywords
On the geodesic flow on CAT(0) spaces
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DOI: 10.1017/etds.2019.52
Abstract: Under certain assumptions on CAT(0) spaces, we show that the geodesic flow is topologically mixing. In particular, the Bowen–Margulis’ measure finiteness assumption used by Ricks [Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow… read more here.
Keywords: cat spaces; geodesic flow; flow cat; bowen margulis ... See more keywords
Some Remarks on High Degree Polynomial Integrals of the Magnetic Geodesic Flow on the Two-Dimensional Torus
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DOI: 10.1134/s0037446621040017
Abstract: We study the magnetic geodesic flow on the two-dimensional torus which admits an additional high degree first integral polynomial in momenta and is independent of the energy integral. In an earlier work by the first two authors, it… read more here.
Keywords: magnetic geodesic; geodesic flow; high degree; two dimensional ... See more keywords