  In presence of unstable dimension variability numerical solutions of chaotic
systems are valid only for short periods of observation. For this reason,
analytical results for systems that exhibit this phenomenon are needed. Aiming
to go one step further in obtaining such results, we study the parametric
evolution of unstable dimension variability in two coupled bungalow maps. Each
of these maps presents intervals of linearity that define Markov partitions,
which are recovered for the coupled system in the case of synchronization.
Using such partitions we find exact results for the onset of unstable dimension
variability and for contrast measure, which quantifies the intensity of the
phenomenon in terms of the stability of the periodic orbits embedded in the
synchronization subspace.
