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 3.1 and 3.2. 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 2:1 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. See also Pulsating white dwarf Pulsating Radio Source Asteroseismology References Variable stars Astrophysics