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arXiv · 2608.22784

$C^1$-robust strong pluripotency for blender-horseshoes

Teruhiko Soma·Shuntaro Tomizawa
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Abstract

Suppose that $M$ is a closed manifold of dimension greater than two. We show that there exists a $C^1$-diffeomorphism $f_0:M\longrightarrow M$ with a wild affine blender-horseshoe $\Lambda_{f_0}$ such that any element $f$ of $\mathrm{Diff}^1(M)$ sufficiently $C^1$-close to $f_0$ is strongly pluripotent for the continuation $\Lambda_f^{(\mathrm{mj})}$ of $\Lambda_{f_0}^{(\mathrm{mj})}$, where $\Lambda_{f_0}^{(\mathrm{mj})}$ is the dense subset of $\Lambda_{f_0}$ consisting of elements with majority condition.

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Teruhiko Soma, Shuntaro Tomizawa. 2026-08-24. $C^1$-robust strong pluripotency for blender-horseshoes. https://arxiv.org/abs/2608.22784

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