A shadowable chain recurrent set with an attached hyperbolic singularity
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866913769828909056 |
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| author | Murakami, Sogo |
| author_facet | Murakami, Sogo |
| contents | We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a four-dimensional sphere whose nonwandering set contains an attached hyperbolic singularity yet possesses the standard shadowing property. This gives a counterexample to a conjecture given by Arbieto, López, Rego and Sánchez (Math. Annalen 390:417-437). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A shadowable chain recurrent set with an attached hyperbolic singularity Murakami, Sogo Dynamical Systems 37C10, 37C50 (Primary) We prove that every factor map between topological flows preserves the standard shadowing property if it is injective except for a closed orbit that shrinks to a singularity. As an application, we construct a $C^\infty$-flow on a four-dimensional sphere whose nonwandering set contains an attached hyperbolic singularity yet possesses the standard shadowing property. This gives a counterexample to a conjecture given by Arbieto, López, Rego and Sánchez (Math. Annalen 390:417-437). |
| title | A shadowable chain recurrent set with an attached hyperbolic singularity |
| topic | Dynamical Systems 37C10, 37C50 (Primary) |
| url | https://arxiv.org/abs/2501.04294 |