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A Dynamical Systems Approach to Nonlinear Stellar Pulsations

  • Chapter
Nonlinear Phenomena in Stellar Variability

Abstract

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 con-vective 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 non ad 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.

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Authors and Affiliations

  1. University of Florida, Gainsville, FL32611, USA

    J. R. Buchler

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  1. J. R. Buchler
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Editors and Affiliations

  1. Astronomical Institute, Tôhoku University, Sendai, Japan

    M. Takeuti

  2. University of Florida, Gainsville, USA

    J.-R. Buchler

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© 1993 Springer Science+Business Media Dordrecht

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Buchler, J.R. (1993). A Dynamical Systems Approach to Nonlinear Stellar Pulsations. In: Takeuti, M., Buchler, JR. (eds) Nonlinear Phenomena in Stellar Variability. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1062-4_2

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  • DOI: https://doi.org/10.1007/978-94-011-1062-4_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4462-2

  • Online ISBN: 978-94-011-1062-4

  • eBook Packages: Springer Book Archive

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