测度中心的M_(α)-跟踪性质

M_(α)-shadowing Property on the Measure Center

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.