  Hundreds of giant planets have been discovered so far and the quest of
exo-Earths in giant planet systems has become intriguing. In this work, we aim
to address the question of the possible long-term coexistence of a terrestrial
companion on an orbit interior to a giant planet, and explore the extent of the
stability regions for both non-resonant and resonant configurations. Our study
focuses on the restricted three-body problem, where an inner terrestrial planet
(massless body) moves under the gravitational attraction of a star and an outer
massive planet on a circular or elliptic orbit. Using the Detrended Fast
Lyapunov Indicator as a chaotic indicator, we constructed maps of dynamical
stability by varying both the eccentricity of the outer giant planet and the
semi-major axis of the inner terrestrial planet, and identify the boundaries of
the stability domains. Guided by the computation of families of periodic
orbits, the phase space is unravelled by meticulously chosen stable periodic
orbits, which buttress the stability domains. We provide all possible stability
domains for coplanar symmetric configurations and show that a terrestrial
planet, either in mean-motion resonance or not, can coexist with a giant
planet, when the latter moves on either a circular or an (even highly)
eccentric orbit. New families of symmetric and asymmetric periodic orbits are
presented for the 2/1 resonance. It is shown that an inner terrestrial planet
can survive long time spans with a giant eccentric outer planet on resonant
symmetric orbits, even when both orbits are highly eccentric. For 22 detected
single-planet systems consisting of a giant planet with high eccentricity, we
discuss the possible existence of a terrestrial planet. This study is
particularly suitable for the research of companions among the detected systems
with giant planets, and could assist with refining observational data.
