Differential Geometry, Billiards, and Geometric Optics / Géométrie différentielle, billards et optique géométrique

Collection Differential Geometry, Billiards, and Geometric Optics / Géométrie différentielle, billards et optique géométrique

Organizer(s) Glutsyuk, Alexey ; Izmestiev, Ivan ; Radnovic, Milena ; Tabachnikov, Sergei

Date(s) 04/10/2021 - 08/10/2021

linked URL https://conferences.cirm-math.fr/2383.html

00:00:00 / 00:00:00

3 5

Geodesic scattering on hyperboloids

By Alexander Veselov

Geodesic flow on ellipsoids is one of the most celebrated classical integrable systems considered by Jacobi in 1837. Moser revisited this problem in 1978 revealing the link with the modern theory of solitons. Surprisingly a similar question for hyperboloids did not get much attention, although the dynamics in this case is very different. I will explain how to use the remarkable results of Moser and Knoerrer on the relations between Jacobi problem and integrable Neumann system on sphere to describe explicitly the geodesic scattering on hyperboloids. It will be shown also that Knoerrer's reparametrisation is closely related to the projectively equivalent metric on a quadric discovered in 1998 by Tabachnikov and, independently, by Matveev and Topalov, giving a new proof of their result. The projectively equivalent metric (in contrast to the usual one) turns out to be regular on the projective closure of hyperboloid, which allows usto extend Knoerrer's map to this closure. The talk is based on a recent joint work with Lihua Wu.

Information about the video

Date of recording 04/10/2021
Date of publication 15/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19820303
Cite this video Veselov, Alexander (04/10/2021). Geodesic scattering on hyperboloids. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19820303
URL https://dx.doi.org/10.24350/CIRM.V.19820303

Domain(s)

Differential Geometry

Bibliography

VESELOV, A. P. et WU, L. H. Geodesic scattering on hyperboloids and Knörrer's map. Nonlinearity, 2021, vol. 34, no 9, p. 5926. - https://arxiv.org/abs/2008.12524

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