Studying hyperbolicity in chaotic systems

On the basis of method [1] proposed for diagnosing 2-dimensional chaotic sa ddles we present a numerical procedure to distinguish hyperbolic and nonhyp erbolic chaotic attractors in three-dimensional flow systems. This techniqu e is based on calculating the angles between stable and unstable manifolds along a chaotic trajectory in R-3. We show for three-dimensional flow syste ms that this serves as an efficient characteristic for exploring chaotic di fferential systems. We also analyze the effect of noise on the structure of angle distribution for both 2-dimensional invertible maps and a 3-dimensio nal continuous system. (C) 2000 Elsevier Science B.V. All rights reserved.