Resumen de Classification and reduction of polynomial Hamiltonians with three degrees of freedon

Susana Gutiérrez Romero, Jesús Francisco Palacián Subiela, Patricia Yanguas Sayas

• We classify all possible normal forms associated with the quadratic part of a polynomial Hamiltonian function in three degrees of freedom (3 DOF). Then we make an analysis based on normalizations which allow us to reduce the number of degrees of freedom at least one unit. We consider an arbitrary polynomial Hamiltonian whose principal part is quadratic in positions and momenta. The procedure is based on the extension of an integral of the unperturbed part to the whole system, up to a certain order. Finally we present some features of an algorithm developed so as to simplify an arbitrary n DOF polynomial Hamiltonian.