  We study anharmonic localization in a periodic five atom chain with
quadratic-quartic spring potential. We use discrete symmetries to eliminate the
degeneracies of the harmonic chain and easily find periodic orbits. We apply
linear stability analysis to measure the frequency of phonon-like disturbances
in the presence of breathers and to analyze the instabilities of breathers. We
visualize the phase plane of breather motion directly and develop a technique
for exciting pinned and moving breathers. We observe long-lived breathers that
move chaotically and a global transition to chaos that prevents forming moving
breathers at high energies.
