AI 中文总结
针对维数大于2的闭流形，本文证明存在带野生仿射blender马蹄的$C^1$微分同胚，其邻近$C^1$微分同胚对对应延拓的稠密子集具有强多能性。
AI 中文摘要
设$M$为维数大于2的闭流形，本文证明存在$C^1$微分同胚$f_0:M\to M$，其带有野生仿射blender马蹄$\Lambda_{f_0}$，且任何与$f_0$充分$C^1$接近的$\mathrm{Diff}^1(M)$中元素$f$，对$\Lambda_{f_0}^{(\text{mj})}$的延拓$\Lambda_f^{(\text{mj})}$具有强多能性，其中$\Lambda_{f_0}^{(\text{mj})}$是$\Lambda_{f_0}$中满足多数条件的元素构成的稠密子集。
英文摘要
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 $Λ_{f_0}$ such that any element $f$ of $\mathrm{Diff}^1(M)$ sufficiently $C^1$-close to $f_0$ is strongly pluripotent for the continuation $Λ_f^{(\mathrm{mj})}$ of $Λ_{f_0}^{(\mathrm{mj})}$, where $Λ_{f_0}^{(\mathrm{mj})}$ is the dense subset of $Λ_{f_0}$ consisting of elements with majority condition.
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