Eigenvectors of lax matrices, spaces of hyperelliptic curves and action coordinates for moser systems

Michèle Audin (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We describe a Poisson structure on some open subset of the relative Jacobian of hyperelliptic curves and use eigenvectors of Lax matrices to derive action variables for Moser systems.

Mots clés: integrable systems; action-angle coordinates; Hurwitz spaces; hyperelliptic curves; Poisson manifolds; Lax pairs; geodesics on quadrics; Moser systems

Domaines: Géométrie différentielle [math.DG]

Michèle Audin. Eigenvectors of lax matrices, spaces of hyperelliptic curves and action coordinates for moser systems. Regular & Chaotic Dynamics, 2000, 5 (1), pp.67-88. ⟨10.1070/RD2000v005n01ABEH000124⟩. ⟨hal-00129630⟩