On the Shadowableness of Flows With Hyperbolic Singularities
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910661578063872 |
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| author | Arbieto, Alexander López, Andrés M. Rego, Elias Sánchez, Yeison |
| author_facet | Arbieto, Alexander López, Andrés M. Rego, Elias Sánchez, Yeison |
| contents | In this work we study the existence of singular flows satisfying shadowing-like properties. More precisely, we prove that if C1 -vector field on a closed manifold induces a chain-recurrent flow containing an attached hyperbolic singularity of stable or unstable index-one, then this flow cannot satisfy the shadowing property. If the manifold is non-compact, the vector field is complete and non-wandering, we prove that we prove that the existence of index-one hyperbolic singularities prevents the induced flow to satisfy the rescaled-shadowing property introduced in [6]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06131 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Shadowableness of Flows With Hyperbolic Singularities Arbieto, Alexander López, Andrés M. Rego, Elias Sánchez, Yeison Dynamical Systems Primary MSC code 37C10, Secondary MSC code 37C50 In this work we study the existence of singular flows satisfying shadowing-like properties. More precisely, we prove that if C1 -vector field on a closed manifold induces a chain-recurrent flow containing an attached hyperbolic singularity of stable or unstable index-one, then this flow cannot satisfy the shadowing property. If the manifold is non-compact, the vector field is complete and non-wandering, we prove that we prove that the existence of index-one hyperbolic singularities prevents the induced flow to satisfy the rescaled-shadowing property introduced in [6]. |
| title | On the Shadowableness of Flows With Hyperbolic Singularities |
| topic | Dynamical Systems Primary MSC code 37C10, Secondary MSC code 37C50 |
| url | https://arxiv.org/abs/2303.06131 |