N-dimension Scattering Chaos And The Property Of Li-Yorke Sensitivity

Chaos theory became a central topic of research since the term of chaos wasintroduced by Li and Yorke in a paper “Period Three Implies chaos” in1975. In1989,Devaney obtained a new notion of chaos called Devaney chaos by using dense periodicpoints, topological transitivity and sensitive dependence on initial values. With thedevelopment of science and technology, the study of chaos has been deep into thevarious fields of natural sciences and social sciences: mathematics, chemistry,astronomy, physics, geological exploration, Electronics and Electrical, economicmanagement, humanities, etc. So, it is necessary to further study chaoticity of dynamics.This paper mainly studies chaos theory and obtain the following results:First, we give a general method of discrete linearization of N dimensional nonlinearautonomous system and the definitions of scattering and weak scattering on theequilibrium points of n-dimensional autonomous system are first given. Meanwhile, asufficient condition on weak scattering is obtained. By using this result, it is proved thatall saddle points are weak scattering points. Finally, we give a criterion and a sufficientand necessary condition on scattering point.Second, we main discuss the properties of Li-Yorke sensitive product map and itsiteration invariance, prove that the Li-Yorke sensitivity is always hold by product mapoperation, so its composite operation is under uniformly continuous sense.