  Context: Resonances in the stellar orbital motion under perturbations from
spiral arms structure play an important role in the evolution of the disks of
spiral galaxies. The epicyclic approximation allows the determination of the
corresponding resonant radii on the equatorial plane (for nearly circular
orbits), but is not suitable in general.
  Aims: We expand the study of resonant orbits by analysing stellar motions
perturbed by spiral arms with Gaussian-shaped profiles without any restriction
on the stellar orbital configurations, and we expand the concept of Lindblad
(epicyclic) resonances for orbits with large radial excursions.
  Methods: We define a representative plane of initial conditions, which covers
the whole phase space of the system. Dynamical maps on representative planes
are constructed numerically, in order to characterize the phase-space structure
and identify the precise location of resonances. The study is complemented by
the construction of dynamical power spectra, which provide the identification
of fundamental oscillatory patterns in the stellar motion.
  Results: Our approach allows a precise description of the resonance chains in
the whole phase space, giving a broader view of the dynamics of the system when
compared to the classical epicyclic approach, even for objects in retrograde
motion. The analysis of the solar neighbourhood shows that, depending on the
current azimuthal phase of the Sun with respect to the spiral arms, a star with
solar kinematic parameters may evolve either inside the stable co-rotation
resonance or in a chaotic zone.
  Conclusions: Our approach contributes to quantifying the domains of resonant
orbits and the degree of chaos in the whole Galactic phase-space structure. It
may serve as a starting point to apply these techniques to the investigation of
clumps in the distribution of stars in the Galaxy, such as kinematic moving
groups.
