| Data: |
1999 |
| Resum: |
The article studies geometrically the Euler-Arnold equations associatedto geodesic flow on SO(4) for a left invariant diagonal metric. Such metric were first introduced by Manakov [17] and extensively studied by Mishchenko-Fomenko [18] andDikii [6]. An essential contribution into the integrability of this problem was also made by Adler-van Moerbeke [4] andHaine [8]. In this problem there are four invariants of the motion defining in C4 = Lie(SO(4) ⊗ C) an affine Abelian surface as complete intersection of four quadrics. The first section is devoted to a Lie algebra theoretical approach, basedon the Kostant-Kirillov coadjoint action. This methodallo ws us to linearizes the problem on a two-dimensional Prym variety Prymσ(C) of a genus 3 Riemann surface C. In section 2, the methodconsists of requiring that the general solutions have the Painlev'e property, i. e. , have no movable singularities other than poles. It was first adopted by Kowalewski [10] andhas developedandusedmore systematically [3], [4], [8], [13]. From the asymptotic analysis of the differential equations, we show that the linearization of the Euler- Arnoldequations occurs on a Prym variety Prymσ(Γ) of an another genus 3 Riemann surface Γ. In the last section the Riemann surfaces are comparedexplicitly . |
| Drets: |
Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.  |
| Llengua: |
Anglès |
| Document: |
Article ; recerca ; Versió publicada |
| Publicat a: |
Publicacions matemàtiques, Vol. 43, Num. 1 (1999) , p. 261-279, ISSN 2014-4350 |
visitant ::
identificació
