  We study the behavior of non-Markovianity with respect to the localization of
the initial environmental state. The "amount" of non-Markovianity is measured
using divisibility and distinguishability as indicators, employing several
schemes to construct the measures. The system used is a qubit coupled to an
environment modeled by an Ising spin chain kicked by ultra-short pulses of a
magnetic field. In the integrable regime, non-Markovianity and localization do
not have a simple relation, but as the chaotic regime is approached, simple
relations emerge, which we explore in detail. We also study the
non-Markovianity measures in the space of the parameters of the spin coherent
states and point out that the pattern that appears is robust under the choice
of the interaction Hamiltonian but does not have a KAM-like phase-space
structure.
