测度中心的M_(α)-跟踪性质  

M_(α)-shadowing Property on the Measure Center

作　　者：吴新星 WU XINXING(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025

出　　处：《应用数学学报》2024年第2期355-368,共14页Acta Mathematicae Applicatae Sinica

基　　金：贵州省高等学校系统建模与数据挖掘重点实验室(批准号:2023013);四川省自然科学基金(批准号:2022NSFSC1821)资助项目。

摘　　要：本文证明如果动力系统具有周期M_(α)-跟踪性质或者周期M^(α)-跟踪性质,则其测度中心的限制系统也具有相同的跟踪性质.反之,如果动力系统在其测度中心的限制系统具有周期M_(α)-跟踪性质(或者,周期M^(α)-跟踪性质),则该动力系统具有周期M_(β)-跟踪性质(相应地,周期M^(β)-跟踪性质),对任意β∈[0,α).同时得到对等度连续系统,众多跟踪性质都等价于动力系统具有平凡的测度中心.In this paper,it is proved that if a dynamical system has the periodic M_(α)-shadowing property or periodic M^(α)-shadowing property,then the dynamical sys-tem restricted on its measure center has the same shadowing property.Conversely,if a dynamical system restricted on its measure center has the periodic M_(α)-shadowing property(resp.,periodic M^(α)-shadowing property),then the dynamical system has the periodic M_(β)-shadowing property(resp.,periodic M^(β)-shadowing property)for anyβe[0,a).Moreover,it is obtained that for an equicontinuous system,many shadowing properties are equivalent to the condition that it has a trivial measure center.

关 键 词：M^(α)-跟踪性质 M_(α)-跟踪性质 测度中心 等度连续 

分 类 号：O189.1[理学—数学]