A DYNAMICAL-SYSTEMS APPROACH TO NONLINEAR STELLAR PULSATIONS

Over the last decade we have seen the application of novel techniques to the old problem of nonlinear stellar pulsations. Together with nume rical hydrodynamics this approach provides a more fundamental understa nding of the systematics of the pulsational behavior. For weakly nonad iabatic pulsations, whether regular or multi-periodic, dimensional red uction techniques lead to amplitude equations and to a description in terms of modal interactions and resonances. In particular they shed ne w light on the bump progression in the classical Cepheids. In more dis sipative stars numerical hydrodynamical modelling has uncovered the ex istence of irregular variability, both in radiative and in convective models. An application of modern dynamical systems techniques has show n that this behavior occurs according to well understood routes from r egular to chaotic behavior. The mechanism is very robust and represent s the first non ad hoc theoretical explanation of irregular stellar va riability. Finally, we discuss how a comparison with observations of i rregular variability shows the need for more suitable observations, on the one hand, and of better techniques of signal processing, on the o ther.