Determining Consecutive Periods of the Lorenz Maps
© FulaiWang. 2010
Received: 18 October 2009
Accepted: 19 May 2010
Published: 16 June 2010
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.
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