  We study the distribution of nearby thick disc and halo stars in subspaces
defined by their characteristic orbital parameters. Our aim is to establish the
origin of the structure reported in particular, in the $R_{\rm max}-z_{\rm
max}$ space. To this end, we compute the orbital parameters and frequencies of
stars for a generic and for a St\"ackel Milky Way potential. We find that for
both the thick disc and halo populations very similar prominent substructures
are apparent for the generic Galactic potential, while no substructure is seen
for the St\"ackel model. This indicates that the origin of these features is
not merger-related, but due to non-integrability of the generic potential. This
conclusion is strengthened by our frequency analysis of the orbits of stars,
which reveals the presence of prominent resonances, with $\sim 30\%$ of the
halo stars associated to resonance families. In fact, the stars in resonances
define the substructures seen in the spaces of characteristic orbital
parameters. Furthermore, we find that some stars in our sample and in debris
streams are on the same resonance as the Sagittarius dwarf, suggesting this
system has also influenced the distribution of stars in the Galactic thick disc
and halo components. Our study constitutes a step towards disentangling the
imprint of merger debris from substructures driven by internal dynamics. Given
their prominence, these resonant-driven overdensities could potentially be
useful to constrain the exact form of the Galactic potential.
