Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion

Harry Braden, Viktor Enolski, Yu. N. Fedorov

Research output: Contribution to journalArticlepeer-review

Abstract

We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves.

Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve.
Original languageEnglish
Pages (from-to)1865-1889
JournalNonlinearity
Volume26
Issue number7
Early online date30 May 2013
DOIs
Publication statusPublished - Jul 2013

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