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

Autor:	Braden, H. W., Enolski, V. Z., Fedorov, Yu. N.
Rok vydání:	2012
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems 70H06 14H42 14H70 37K10
Druh dokumentu:	Working Paper
DOI:	10.1088/0951-7715/26/7/1865
Popis:	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. Comment: 22 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1210.3596 Zobrazit plný text záznamu View this record from Arxiv