Astrophysics and Space Science

, Volume 210, Issue 1–2, pp 9–31 | Cite as

A dynamical systems approach to nonlinear stellar pulsations

  • J. R. Buchler
I. Fundamental Theories


Over the last decade we have seen the application of novel techniques to the old problem of nonlinear stellar pulsations. Together with numerical hydrodynamics this approach provides a more fundamental understanding of the systematics of the pulsational behavior. For weakly nonadiabatic pulsations, whether regular or multi-periodic, dimensional reduction techniques lead to amplitude equations and to a description in terms of modal interactions and resonances. In particular they shed new light on the bump progression in the classical Cepheids. In more dissipative stars numerical hydrodynamical modelling has uncovered the existence of irregular variability, both in radiative and in convective models. An application of modern dynamical systems techniques has shown that this behavior occurs according to well understood routes from regular to chaotic behavior. The mechanism is very robust and represents the first nonad hoc theoretical explanation of irregular stellar variability. Finally, we discuss how a comparison with observations of irregular variability shows the need for more suitable observations, on the one hand, and of better techniques of signal processing, on the other.


Dimensional Reduction Hydrodynamical Modelling Chaotic Behavior Modal Interaction Theoretical Explanation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • J. R. Buchler
    • 1
  1. 1.University of FloridaGainsvilleUSA

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