Partially chaotic orbits in a perturbed cubic force model

MUZZIO, J. C.

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY

WILEY-BLACKWELL PUBLISHING, INC

Año: 2017 vol. 471 p. 4099 - 4110

0035-8711

pre.cjk { font-family: "Nimbus Mono L",monospace; }p { margin-bottom: 0.25cm; line-height: 120%; }Three types of orbits are theoretically possible in autonomous Hamiltoniansystems with three degrees of freedom: fully chaotic (they only obey theenergy integral), partially chaotic (they obey an additional isolatingintegral besides energy) and regular (they obey two isolating integralsbesides energy). The existence of partially chaotic orbits has been deniedby several authors, however, arguing either that there is a sudden transitionfrom regularity to full chaoticity, or that a long enough follow up of asupposedly partially chaotic orbit would reveal a fully chaotic nature. Thissituation needs clarification, because partially chaotic orbits might play asignificant role in the process of chaotic diffusion. Herewe use numerically computed Lyapunov exponents to explore the phasespace of a perturbed three dimensional cubic force toy model, and ageneralization of the Poincar´e maps to show that partially chaotic orbitsare actually present in that model. They turn out to be double orbits joinedby a bifurcation zone, which is the most likely source of their chaos, andthey are encapsulated in regions of phase space bounded by regular orbitssimilar to each one of the components of the double orbit.