We construct open sets of degenerate unfoldings of heterodimensional cycles of any co-index \(c>0\) and homoclinic tangencies of arbitrary codimension \(c>0\). These type of sets are known to be the support of unexpected phenomena in families of diffeomorphisms, such as the Kolmogorov typical co-existence of infinitely many attractors. As a prerequisite, we also construct robust homoclinic tangencies of large codimension which cannot be inside a strong partially hyperbolic set.

中文翻译：

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循环和切线的健壮简并展开

我们构造了任意共指数\（c> 0 \）和任意余维\（c> 0 \）的同斜切线的异维周期的简并展开的开放集合。已知这些类型的集是微亚纯族中意外现象的支持，例如无限多吸引子的Kolmogorov典型共存。作为前提，我们还构造了大共维数的稳健的同斜切线，这些切线不能在强局部双曲集中。