We classify the possible normal forms of quadratic Hamiltonians in 2 dimensions. Then we give a method to reduce by one the number of degrees of freedom of an arbitrary polynomial Hamiltonian whoseâ€¦ (More)

Axially symmetric perturbations of the isotropic harmonic oscillator in three dimensions are studied. A normal form transformation introduces a second symmetry, after truncation. The reduction of theâ€¦ (More)

We classify the normal forms associated to polynomial vector fields with dimensions two and three whose principal part is linear. Then we reduce by one the dimension of the associated differentialâ€¦ (More)

We investigate the dynamics of various problems defined by Hamiltonian systems of two and three degrees of freedom that have in common that they can be reduced by an axial symmetry. Specifically, theâ€¦ (More)

We depart from an n-degree-of-freedom Hamiltonian formed by the sum of homogeneous polynomials in n coordinates and n momenta with arbitrary coefficients. By extending formally an integral of theâ€¦ (More)

We consider a family of three-degree-of-freedom (3-DOF) Hamiltonian systems defined by a Taylor expansion around an elliptic equilibrium. More precisely, the system is a perturbed harmonic oscillatorâ€¦ (More)