  It has been shown that the dissipative gas infall during galaxy formation has
the capability to modify the shape of dark matter halos. In this paper we
perform the first detailed analysis of particle orbits in a cosmological dark
matter halos to understand {\it how} and {\it why} baryons alter its shape. We
perform a series of numerical experiments where we grow a baryonic core inside
a live dark matter halo extracted from a cosmological simulation. We follow the
orbits of more than 300 particles with more that 50000 timesteps. Our results
clearly show that the dissipational component is responsible for repeatedly
deflecting orbits which visit often the center of the system. Moreover the
gravitational potential time dependence associated with the growth of the
baryonic mass, shifts the frequencies of the orbits, making them extremely
chaotic. This randomization makes the orbits explore a large phase space. When
this effect takes place for a significant number of orbits it will be
manifested in the density distribution as an approach to a rounder
configuration. As a consequence, the influence of the central mass on the shape
of the phase space decreases with increasing distance from the center. We
discuss the importance of future analysis of controlled experiments (i.e. using
analytic potentials instead of live DM halos) to better decipher the dynamics
of this phenomenon.
