LOCAL FALSE NEAREST NEIGHBORS AND DYNAMIC DIMENSIONS FROM OBSERVED CHAOTIC DATA

The time delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer embedding dimension. The minimum necessary global embedding dimension d(E) may still be larger than the actual dimension of the underlying dynamics d(L). The embedding theorem only guarantees that the attractor of the system is fully unfolded using d(E) greater than 2d(A), with d(A) the fractal attractor dimension. Using the idea of local false nearest neighbors, we discuss methods for determining the integer-valued d(L).