  Many chaotic dynamical systems of physical interest present a strong form of
nonhyperbolicity called unstable dimension variability (UDV), for which the
chaotic invariant set contains periodic orbits possessing different numbers of
unstable eigendirections. The onset of UDV is usually related to the loss of
transversal stability of an unstable fixed point embedded in the chaotic set.
In this paper, we present a new mechanism for the onset of UDV, whereby the
period of the unstable orbits losing transversal stability tends to infinity as
we approach the onset of UDV. This mechanism is unveiled by means of a periodic
orbit analysis of the invariant chaotic attractor for two model dynamical
systems with phase spaces of low dimensionality, and seems to depend heavily on
the chaotic dynamics in the invariant set. We also described, for these
systems, the blowout bifurcation (for which the chaotic set as a whole loses
transversal stability) and its relation with the situation where the effects of
UDV are the most intense. For the latter point, we found that chaotic
trajectories off, but very close to, the invariant set exhibit the same scaling
characteristic of the so-called on-off intermittency.
