  We investigate the interplay between jets from Active Galactic Nuclei (AGNs)
and the surrounding InterStellar Medium (ISM) through full 3D, high resolution,
Adaptive Mesh Refinement simulations performed with the FLASH code. We follow
the jet- ISM system for several Myr in its transition from an early, compact
source to an extended one including a large cocoon. During the jet evolution,
we identify three major evolutionary stages and we find that, contrary to the
prediction of popular theoretical models, none of the simulations shows a
self-similar behavior. We also follow the evolution of the energy budget, and
find that the fraction of input power deposited into the ISM (the AGN coupling
constant) is of order of a few percent during the first few Myr. This is in
broad agreement with galaxy formation models employing AGN feedback. However,
we find that in these early stages, this energy is deposited only in a small
fraction (< 1%) of the total ISM volume. Finally we demonstrate the relevance
of backflows arising within the extended cocoon generated by a relativistic AGN
jet within the ISM of its host galaxy, previously proposed as a mechanism for
self-regulating the gas accretion onto the central object. These backflows tend
later to be destabilized by the 3D dynamics, rather than by hydrodynamic
(Kelvin- Helmholtz) instabilities. Yet, in the first few hundred thousand
years, backflows may create a central accretion region of significant extent,
and convey there as much as a few millions of solar masses.
