2019/08/26 by Khan, Abdul Gaffar, Das, Tarun
#37C50 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 54H20 #Secondary: 37C75
paper · doi:10.48550/arxiv.1908.09536
We introduce minimally expansive and GH-stable points for homeomorphisms on metric spaces and μ-uniformly expansive, μ-shadowable and strong μ-topologically stable points for Borel measures (with respect to a homeomorphism on a metric space). We prove that: (i) minimally expansive shadowable point of a homeomorphism on a compact metric space is topologically stable and GH-stable. (ii) μ-uniformly expansive μ-shadowable point for a Borel measure μ (with respect to a homeomorphism on a compact metric space) is strong μ-topologically stable.