A novel algorithm for calculating the smallest Liapunov exponent

Presented in this paper is a very simple algorithm for calculating the smallest Liapunov exponent for any n-dimensional attractor. The key idea lies in the fact that as the direction of motion is reversed, an attractor is changed into a repellor. Then the smallest Liapunov exponent with a minus sign becomes the largest Liapunov exponent of the new orbit and can be easily determined. This idea can be used to calculate other Liapunov exponents for orbits in high dimensional state space. The algorithm can be applied to both continuous and discrete systems.