ABSTRACT
The chapter explains the theory of singular system analysis, a generalization of eigenfunction analysis, with particular reference to its use for extending the concepts of classical information theory. The classical theory of information is reviewed based upon an eigenvalue inversion in an L space of a first kind Fredholm equation. Broomhead and King have used the singular system analysis to construct an embedding of the global attractor. The measures of information content or number of degrees of freedom which the theory provides have been used to analyse time series data from nonlinear dynamical systems. The number of degrees of freedom that results from the singular system analysis identifies the dimension of a deterministic subspace. The singular system analysis offers a new direction in the treatment of data from that of conventional Fourier or correlation processing. A local analysis in this reduced space was then used to discover the underlying dimension or number of independent processes contributing to the motion.
