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A shortcut to the Kovalevskaya curve

Banff International Research Station for Mathematical Innovation and Discovery

There have already been numerous studies and interpretations of the famous separation of variables in the integrable top of S. Kovalevskaya. In this talk we show how the original Kovalevskaya curve of separation can be obtained, by a simple one-step transformation, from the spectral curve of the Lax representation found by Bobenko, Reyman, and Semenov-Tian-Shansky. The algorithm works for the general constants of motion of the top and is based on W. Barth's description of Prym varieties via pencils of genus 3 curves. This also allows us to derive existing and new curves of separation for the Kovalevskaya gyrostat in one and two force fields.

Mathematics; Dynamical systems and ergodic theory; Ordinary differential equations; Dynamical systems

video/mp4

Author affiliation: Universitat Politechnica de Catalunya

2017-01-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60032

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/