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arXiv · 2103.11964

Historic wandering domains near cycles

Pablo G. Barrientos
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Abstract

We explain how to obtain non-trivial historic contractive wandering domains for a dense set of diffeomorphisms in certain type of $C^r$-Newhouse domains of homoclinic tangencies in dimension $d\geq 3$ and $r\geq 1$. In particular, this gives for the first time a contribution to Takens' last problem in the $C^1$ topology and in dimension $d>2$. We show how these Newhouse domains can be obtained arbitrarily close to diffeomorphisms exhibiting heterodimensional cycles (in dimension $d=3$) or non-transverse equidimensional cycles (in any dimension $d\ge 3$) associated with periodic points with non-real complex leading multipliers.

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Pablo G. Barrientos. 2021-03-22. Historic wandering domains near cycles. https://doi.org/10.1088/1361-6544/ac6371

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