Study Enough-Requirement Of Li-Yorke Chaos

The proposition of modern Chaos theory and model, has advanced the scientific research of each field greatly. The scholars have done a large amount of to study and make the abundant achievement to the Chaos phenomenon, the theoretical system of the Chaos is being improved constantly. However, what is the Chaos? There is no identical strict definition. In 1975, T.Y.Li and J.A.Yorke have proposition the concepts of "Chaos". So research and improvement of Li-Yorke Chaos have been fast growing in near these decades and become the branch that can't ignore in the field of dynamical system. And, because the characteristic of the one dimensional dynamical system and topological property on interval, so, it fast growing on research of the Chaotic continuous self-maps on interval. But it is not very overall that the method to judge whether continuous self-maps on interval becomes Li-Yorke Chaotic maps and it await to improve and upgrade and break through. Based on the predecessor's researches, this thesis develops a new method of my own to classify the characteristics of theω-limit point locus into various cases by the analytic ways and studies the enough-conditions of the continuous self-maps on interval becomes Chaotic maps from the angle of those characteristics. In this way some enough-conditions are put forward. Thus it has improved that a fresh way is furnished to reveal the essence of chaotic phenomena1.