Simonetta ABENDA

Dipartimento di Matematica & C.I.R.A.M., 
Università di Bologna, 
Piazza San Donato 5, I
40127 Bologna    Italie

abenda@ciram.ing.unibo.it

Geometric characterisation of integrability of a class of hamiltonian systems

Abstract: We consider so called hyperelliptically separable systems (h.s.s.) arising in various physical problems whose generic inviariant manifolds are open subsets of strata of hyperelliptic Jacobians or their coverings. It turns out that algebraic geometrical structure of such systems has much in common with that of algebraic completely integrable systems (a.c.i.s.). Using this property we study formal singular solutions of a.c.i.s. and h.s.s. and give estimates for the number and leading behaviour of their principal and lower balances.This can be regarded as a useful extension of Kowalewski- Painlevé integrability test. Some model examples are considered, such as generalizations of the integrable case of the Henon-Heiles system.This can be regarded as a useful extension of Kowalewski-Painlevé integrability test. Some model examples are considered, such as generalizations of the integrable case of the Henon-Heiles system.