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arXiv · 2507.03982

Topological $(\mathscr{F},\mathscr{G})-$shadowing property

Shital H. Joshi·Ekta Shah
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Abstract

We define the concept of $(\mathscr{F},\mathscr{G})-$shadowing property on uniform space and say it as a topological $(\mathscr{F},\mathscr{G})-$shadowing property. We show that topological shadowing, topological $(\mathscr{D},\mathscr{F}_t)-$shadowing, topological $(\mathscr{F}_t,\mathscr{F}_t)-$shadowing and topological $(\mathbb{N},\mathscr{F}_t)-$shadowing are equivalent in compact chain recurrent dynamical system. We also prove that if minimal points of $f$ are not dense in $X$ then the system does not have $(\mathscr{P}(\mathbb{N}),\mathscr{F}_{ps})-$shadowing.

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Shital H. Joshi, Ekta Shah. 2025-07-05. Topological $(\mathscr{F},\mathscr{G})-$shadowing property. https://arxiv.org/abs/2507.03982

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