L-shadowing for the induced hyperspace homeomorphism
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912755694436352 |
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| author | Antunes, Mayara Carvalho, Bernardo Cordeiro, Welington |
| author_facet | Antunes, Mayara Carvalho, Bernardo Cordeiro, Welington |
| contents | We prove that a homeomorphism f of a compact metric space X satisfies the L-shadowing property if and only if its induced hyperspace homeomorphism also satisfies the L-shadowing property. In the proof, assuming only the L-shadowing property, we obtain the existence of points in the asymptotic local-product-structure with iterates approaching in a uniform rate of convergence to zero. This contrasts with the lack of uniformity of contraction on local stable/unstable sets on many homeomorphisms with the L-shadowing property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | L-shadowing for the induced hyperspace homeomorphism Antunes, Mayara Carvalho, Bernardo Cordeiro, Welington Dynamical Systems We prove that a homeomorphism f of a compact metric space X satisfies the L-shadowing property if and only if its induced hyperspace homeomorphism also satisfies the L-shadowing property. In the proof, assuming only the L-shadowing property, we obtain the existence of points in the asymptotic local-product-structure with iterates approaching in a uniform rate of convergence to zero. This contrasts with the lack of uniformity of contraction on local stable/unstable sets on many homeomorphisms with the L-shadowing property. |
| title | L-shadowing for the induced hyperspace homeomorphism |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2512.08677 |