Abstract
The stability properties of nonlinear periodic stellar pulsations are studied within the amplitude equation formalism. Both nonresonant and resonant pulsations are considered. A comparison to a sequence of classical Cepheid models shows that the formalism provides a good qualitative and quantitative description of the behavior of the Floquet coefficients and that it also captures the most important features of the Floquet eigenvectors. It thus helps shed new light on the behaviour (bifurcations) of pulsating stars. In addition, the predictive powers of the analytical approach allow a systematic search for models with specific pulsational properties
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