Exterior algebra-based algorithms to estimate Liapunov spectra and stretching statistics in high-dimensional and distributed systems

摘要

This article introduces a direct method for the numerical estimation of the spectra of Liapunov exponents based on the exterior algebra of measure elements. This approach is computationally more robust than the classical approach based on the evolution of n vectors initially possessing linear independence. Several applications of the method proposed are discussed in connection with finite-dimensional systems exhibiting hyperchaos as well as distributed parameter systems associated with reaction/diffusion kinetics.