A robust obstruction to full strong pluripotency for wild blender-horseshoes
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911625536077824 |
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| author | Kiriki, Shin Li, Xiaolong Nakano, Yushi Soma, Teruhiko |
| author_facet | Kiriki, Shin Li, Xiaolong Nakano, Yushi Soma, Teruhiko |
| contents | Suppose that $M$ is a closed manifold of dimension greater than two and $r\geq 2$. We show that there exists a $C^r$-diffeomorphism $f:M\longrightarrow M$ with a wild affine blender-horseshoe $Λ_f$ which is $C^r$-robustly and strongly pluripotent for $Λ_f^{(\mathrm{mj})}$ but not for $Λ_f$, where $Λ_f^{(\mathrm{mj})}$ is the subset of $Λ_f$ consisting of elements with the majority condition. Thus, within the present affine blender-horseshoe family in [KNS], there is a robust obstruction to extending the strong pluripotency from $Λ_f^{(\mathrm{mj})}$ to the whole horseshoe. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24063 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A robust obstruction to full strong pluripotency for wild blender-horseshoes Kiriki, Shin Li, Xiaolong Nakano, Yushi Soma, Teruhiko Dynamical Systems Primary: 37C20, 37C29, Secondary: 37C25 Suppose that $M$ is a closed manifold of dimension greater than two and $r\geq 2$. We show that there exists a $C^r$-diffeomorphism $f:M\longrightarrow M$ with a wild affine blender-horseshoe $Λ_f$ which is $C^r$-robustly and strongly pluripotent for $Λ_f^{(\mathrm{mj})}$ but not for $Λ_f$, where $Λ_f^{(\mathrm{mj})}$ is the subset of $Λ_f$ consisting of elements with the majority condition. Thus, within the present affine blender-horseshoe family in [KNS], there is a robust obstruction to extending the strong pluripotency from $Λ_f^{(\mathrm{mj})}$ to the whole horseshoe. |
| title | A robust obstruction to full strong pluripotency for wild blender-horseshoes |
| topic | Dynamical Systems Primary: 37C20, 37C29, Secondary: 37C25 |
| url | https://arxiv.org/abs/2604.24063 |