The following shows a similar visualization of the period doubling cascade to chaos for a sequence of stellar models that differ by their average surface temperature T. The presence of low dimensional chaos is also confirmed by another, more sophisticated, analysis of the model pulsations which extracts the lowest unstable periodic orbits and examines their topological organization twisting. The underlying attractor is found to be banded like the Roessler attractor , with however an additional twist in the band.
Takens' theorem guarantees that under very general circumstances the topological properties of this reconstructed evolution operator are the same as that of the physical system, provided the embedding dimension N is large enough. Thus from the knowledge of a single observed variable one can infer properties about the real physical system which is governed by a number of independent variables.
This approach has been applied to the AAVSO data for the star R Scuti   It could be inferred that the irregular pulsations of this star arise from an underlying 4-dimensional dynamics. Phrased differently this says that from any 4 neighboring observations one can predict the next one. From a physical point of view it says that there are 4 independent variables that describe the dynamic of the system.
The method of false nearest neighbors corroborates an embedding dimension of 4.
The fractal dimension of the dynamics of R Scuti as inferred from the computed Lyapunov exponents lies between 3. From an analysis of the fixed points of the evolution operator a nice physical picture can be inferred, namely that the pulsations arise from the excitation of an unstable pulsation mode that couples nonlinearly to a second, stable pulsation mode which is in a resonance with the first one , a scenario described by the Shilnikov theorem.
This resonance mechanism is not limited to R Scuti, but has been found to hold for several other stars for which the observational data are sufficiently good. From Wikipedia, the free encyclopedia. This article has multiple issues. Please help improve it or discuss these issues on the talk page.
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Challenges In Stellar Pulsation
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Evidence for Low-dimensional Chaos in Semiregular Variable Stars
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Frontiers | An Observer's View on the Future of Asteroseismology | Astronomy and Space Sciences
Acquista eBook - 2. Stellar Pulsation - Nonlinear Studies.
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Mine Takeuti , Dimitar D. Stellar pulsations provide a complex system in stars.
Stellar Pulsation Theory
This complexity is studied by analyzing the non-sinusoidal, semi-regular, or irregular light curves. This unique volume summarizes the application of recent theoretical results obtained from stellar pulsation studies. In addition, the latest developments in hydrodynamic simulations are discussed. A historical sketch of the study of beat Cepheids, first known for their variable amplitudes, is given as an introduction to the book. This introduction clearly demonstrates how complicated the study of variable stars can be, and therefore challenges and invites the reader to study the entire book.