Topological $(\mathscr{F},\mathscr{G})-$shadowing property
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916826771881984 |
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| author | Joshi, Shital H. Shah, Ekta |
| author_facet | Joshi, Shital H. Shah, Ekta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological $(\mathscr{F},\mathscr{G})-$shadowing property Joshi, Shital H. Shah, Ekta Dynamical Systems 37B05, 37B65, 37B99 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. |
| title | Topological $(\mathscr{F},\mathscr{G})-$shadowing property |
| topic | Dynamical Systems 37B05, 37B65, 37B99 |
| url | https://arxiv.org/abs/2507.03982 |