Stability Theorems in Pointwise Dynamics

Abdul Gaffar Khan; Tarun Das

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arXiv · 1908.09536

Stability Theorems in Pointwise Dynamics

Abdul Gaffar Khan·Tarun Das

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Abstract

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.

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Abdul Gaffar Khan, Tarun Das. 2019-08-26. Stability Theorems in Pointwise Dynamics. https://arxiv.org/abs/1908.09536

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