Hans Maassen, Madalin Guta, Dmitri Botvich Stability of Bose dynamical systems and branching theory (336K, PostScript) ABSTRACT. Stability under small nonlinear perturbations is proved for a class of linear quantum dynamical systems, including the harmonic oscillator coupled to a free Bose field and the infinite harmonic chrystal. The main tool is an estimate of Dyson's time-dependent perturbation series, based on a labeling of its terms by rooted trees.