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Topological $(\mathscr{F},\mathscr{G})-$shadowing property (2507.03982v1)

Published 5 Jul 2025 in math.DS

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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