Geometric Study of a Family of Integrable Systems

Abstract

The aim of this paper is to demonstrate the rich interaction between complex algebraic geometry,

the theory of integrable systems and the geometry of its asymptotic solutions.We present a family

of integrable hamiltonian systems. We study theses systems from a different angle, assemble

different geometric methods and several views.

Keywords

• Integrable systems,gap theory,abelian varieties,jacobian varieties,embeddings

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