Numerical identification of nonhyperbolicity of the Lorenz system through Lyapunov vectors

Abstract

Understanding nonhyperbolicity in dynamical systems is important, yet, it is usually difficult to see whether a system is hyperbolic or not. In this letter, angles between stable and unstable directions on a point of a chaotic attractor of the Lorenz system with some sets of various parameter values are calculated through identifying Lyapunov vectors numerically. Then we estimate the parameter value where the system becomes nonhyperbolic in one parameter family.