Determining Consecutive Periods of the Lorenz Maps

Abstract

Abstract Based on symbolic dynamics, the paper provides a satisfactory and necessary condition of existence for consecutive periodic orbits of the Lorenz maps. In addition, a new algorithm with computer assistance based on symbolic dynamics is proposed to find all periodic orbits up to a certain number with little computer time. Examples for consecutive periods of orbits are raised for the Lorenz maps. With a little variation, the theorems and algorithm can be applied to some other dynamic systems.