Title: Secondary resonances and the boundary of effective stability of Trojan motions,
Abstract: One of the most interesting features in the libration domain of co-orbital
motions is the existence of secondary resonances. For some combinations of
physical parameters, these resonances occupy a large fraction of the domain of
stability and rule the dynamics within the stable tadpole region. In this work,
we present an application of a recently introduced `basic Hamiltonian model' Hb
for Trojan dynamics, in Paez and Efthymiopoulos (2015), Paez, Locatelli and
Efthymiopoulos (2016): we show that the inner border of the secondary resonance
of lowermost order, as defined by Hb, provides a good estimation of the region
in phase-space for which the orbits remain regular regardless the orbital
parameters of the system. The computation of this boundary is straightforward
by combining a resonant normal form calculation in conjunction with an
`asymmetric expansion' of the Hamiltonian around the libration points, which
speeds up convergence. Applications to the determination of the effective
stability domain for exoplanetary Trojans (planet-sized objects or asteroids)
which may accompany giant exoplanets are discussed.