and therefore there exists no center manifold. Various mechanisms have been proposed, but are found lacking. One, suggests the presence of several closely spaced pulsation frequencies that would beat against each other, but no such frequencies exist in the appropriate stellar models. Another, more interesting suggestion is that the variations are of a stochastic nature, but no mechanism has been proposed or exists that could provide the energy for such large observed amplitude variations. It is now established that the mechanism behind the irregular light curves is an underlying low dimensional chaotic dynamics (see also Chaos theory). This conclusion is based on two types of studies. CFD simulations The computational fluid dynamics numerical forecasts for the pulsations of sequences of W Virginis stellar models exhibit two approaches to irregular behavior that are a clear signature of low dimensional chaos. The first indication comes from first return maps in which one plots one maximum radius, or any other suitable variable, versus the next one. The sequence of models shows a period doubling bifurcation, or cascade, leading to chaos. The near quadratic shape of the map is indicative of chaos and implies an underlying horseshoe map. Other sequences of models follow a somewhat different route, but also to chaos, namely the Pommeau–Manneville or tangent bifurcation route. 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 graph shows triplets of values of the stellar radius (Ri, Ri+1, Ri+2) where the indices i, i+1, i+2 indicate successive time intervals. 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. Global flow reconstruction from observed light curves The method of global flow reconstruction uses a single observed signal {si} to infer properties of the dynamical system that generated it. First N-dimensional 'vectors' are constructed. The next step consists in finding an expression for the nonlinear evolution operator that takes the system from time to time , i.e., . 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