The Chaos Of3-adic System And Time-varying Systems

In this paper, the chaos of3-adic system and time-varying discrete dynamical systemsare studied. Some important results are obtained. Firstly, let (Z (3),τ)be a3-adic system.We prove in (Z (3),τ)the existence of uncountable distributional chaotic set of A(τ), whichis an almost periodic points set, and further come to a conclusion that τ is chaotic in thesense of Devaney and Wiggins. Secondly, some basic concepts are introduced for generaltime-varying systems, including distributional chaos in a sequence, weakly topologicallymixing, and topological mixing. We prove that two uniformly topologically equiconjugatetime-varying systems have the same distributively chaos in a sequence and weaklytopologically mixing. In the end, we give an example of distributional chaos in a sequence offinite dimensional linear time-varying dynamical systems, which can not be distributionallychaotic of type i (i=1,2).