离散动力系统上的一致收敛与传递集  

Uniform Convergence and Transitive Sets on Discrete Dynamical Systems

作　　者：胡印华 邢秋菊 

机构地区：[1]南昌航空大学数学与信息科学学院,江西 南昌

出　　处：《理论数学》2025年第2期153-159,共7页Pure Mathematics

摘　　要：本文主要讨论离散动力系统上一致收敛与传递集的关系。设(X,d)是一个紧致度量空间,fn:X→X是X上的连续自映射序列,并一致收敛于一个连续自映射f。结果表明,当limm→∞d∞(fnm,fm)=0时,若X的非空闭子集A是(X,fn)的传递集,则A是(X,f)的传递集;若X的非空闭子集A是(X,fn)的弱混合集,则A是(X,f)的弱混合集。In this paper, we mainly study the uniform convergence and transitive sets of discrete dynamical systems. Let X be a compact metric space with metric d, and fn:X→Xbe a continuous self-map sequence on X such that (fn)converges uniformly to a continuous self-map f. It is shown that under the condition limm→∞d∞(fnm,fm)=0, let A be a closed subset of X, if A is a transitive set of (X,fn), then A is a transitive set of (X,f);if A is a weakly mixing set of (X,fn), then A is a weakly mixing set of (X,f).

关 键 词：传递集 弱混合集 一致收敛 

分 类 号：O15[理学—数学]