非自治动力系统的多重传递集

Multi-Transitivity Set for Nonautonomous Dynamical Systems

摘要: 基于非自治离散动力系统之间的相互作用，本文主要研究了两个共轭的非自治动力系统(X,f_1,∞)和(Y,g_1,∞)之间的关系。本文首先介绍了非自治动力系统的一些基本概念，主要包括弱混合集、传递集和多重传递集。然后，我们证明了如果A是(X,f_1,∞)的多重传递集，则h(A)是(Y,g_1,∞)的多重传递集。我们把非自治动力系统(X,f_1,∞)的传递集推广到系统(X,f_1,∞)的多重传递集。

Abstract: Based on the interaction between nonautonomous discrete dynamical systems, this paper mainly studies the relationship between two conjugated nonautonomous dynamical systems (X,f_1,∞) and (Y,g_1,∞). We firstly introduced some basic concepts of nonautonomous dynamical systems, mainly including weakly mixed sets, transitive sets, and multi-transitive sets. Then, we proved that if A is a multi-transitive set of (X,f_1,∞), then h(A) is a multi-transitive set of (Y,g_1,∞). We generalized the transitive set of nonautonomous dynamical system   to the fact that system (X,f_1,∞) is a multi-transitive set.