Partially chaotic orbits in a perturbed cubic force model
  Three types of orbits are theoretically possible in autonomous Hamiltonian
systems with three degrees of freedom: fully chaotic (they only obey the energy
integral), partially chaotic (they obey an additional isolating integral
besides energy) and regular (they obey two isolating integrals besides energy).
The existence of partially chaotic orbits has been denied by several authors,
however, arguing either that there is a sudden transition from regularity to
full chaoticity, or that a long enough follow up of a supposedly partially
chaotic orbit would reveal a fully chaotic nature. This situation needs
clarification, because partially chaotic orbits might play a significant role
in the process of chaotic diffusion. Here we use numerically computed Lyapunov
exponents to explore the phase space of a perturbed three dimensional cubic
force toy model, and a generalization of the Poincar\'e maps to show that
partially chaotic orbits are actually present in that model. They turn out to
be double orbits joined by a bifurcation zone, which is the most likely source
of their chaos, and they are encapsulated in regions of phase space bounded by
regular orbits similar to each one of the components of the double orbit.
