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arXiv · 2604.24063

A robust obstruction to full strong pluripotency for wild blender-horseshoes

Shin Kiriki·Xiaolong Li·Yushi Nakano·Teruhiko Soma
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Abstract

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 $\Lambda_f$ which is $C^r$-robustly and strongly pluripotent for $\Lambda_f^{(\mathrm{mj})}$ but not for $\Lambda_f$, where $\Lambda_f^{(\mathrm{mj})}$ is the subset of $\Lambda_f$ 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 $\Lambda_f^{(\mathrm{mj})}$ to the whole horseshoe.

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Shin Kiriki, Xiaolong Li, Yushi Nakano, Teruhiko Soma. 2026-04-27. A robust obstruction to full strong pluripotency for wild blender-horseshoes. https://arxiv.org/abs/2604.24063

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