  We have studied two complementary decoherence measures purity and fidelity
for a generic diffusive noise in two different chaotic systems (the baker and
the cat maps). For both quantities, we have found classical structures in
quantum mechanics - the scar functions - that are specially stable when
subjected to environmental perturbations. We show that these quantum states
constructed on classical invariants are the most robust significant quantum
distributions in generic dissipative maps.
