6 research outputs found
Symbolic dynamics in a binary asteroid system
We highlight the existence of a topological horseshoe arising from a
a--priori stable model of the binary asteroid dynamics. The inspection is
numerical and uses correctly aligned windows, as described in a recent paper by
A. Gierzkiewicz and P. Zgliczy\'nski, combined with a recent analysis of an
associated secular problem.Comment: 20 pages, 10 figure
Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems
We investigate the dynamics of small trojan exoplanets in domains of
secondary resonances within the tadpole domain of motion. We consider the limit
of a massless trojan companion of a giant planet. Without other planets, this
is a case of the elliptic restricted three body problem (ERTBP). The presence
of more planets (the restricted multi-planet problem, RMPP) induces new direct
and indirect secular effects on the trojan's dynamics. In the theoretical part
of this paper, we develop a Hamiltonian formalism in action-angle variables,
which allows to treat in a unified way resonant dynamics and secular effects on
the trojan body in both the ERTBP or the RMPP. Our formalism leads to a
decomposition of the Hamiltonian in two parts, . , called
the basic model, describes resonant dynamics in the short-period (epicyclic)
and synodic (libration) degrees of freedom. contains only terms
depending on slow (secular) angles. is formally identical in the ERTBP
and the RMPP, apart from a re-definition of angular variables. An important
physical consequence is that the slow chaotic diffusion proceeds in both the
ERTBP and the RMPP by a qualitatively similar dynamical mechanism better
approximated by the paradigm of `modulational diffusion'. In the numerical
part, we focus on the ERTBP for making a numerical demonstration of the chaotic
diffusion process along resonances. Using color stability maps, we provide a
survey of the resonant web for characteristic mass parameters of the primary,
in which the secondary resonances from 1:5 to 1:12 (ratio of the short over the
synodic period) and their resonant multiplets appear. We give numerical
examples of diffusion of weakly chaotic orbits in the resonant web. We make a
statistics of the escaping times in the resonant domain, and find power-law
tails of the distribution of escaping times for slowly diffusing chaotic
orbits.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom