Hamiltonian Systems

Zusammenfassung

This chapter is devoted to explaining some concepts and results on Hamiltonian systems. We focus our attention on the concept of complete integrability i.e., Liouville integrability: the existence of n independent first integrals in involution, n being the number of degrees of freedom. Although integrability is well defined for these systems, it is very important to clarify what kind of regularity is allowed for the first integrals: differentiability or analyticity in the real situation, analytic, meromorphic or algebraic (meromorphic and meromorphic at infinity) first integrals in the complex setting.