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arXiv · 2404.08989

High order homoclinic tangencies of corank 2

Dmitrii Mints
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Abstract

We prove that in the space of $C^r$ maps $(r=2,\ldots,\infty,\omega)$ of a smooth manifold of dimension at least 4 there exist open regions where maps with infinitely many corank-2 homoclinic tangencies of all orders are dense. The result is applied to show the existence of maps with universal two-dimensional dynamics, i.e. maps whose iterations approximate the dynamics of every map of a two-dimensional disk with an arbitrarily good accuracy. We show that maps with universal two-dimensional dynamics are $C^r$-generic in the regions under consideration.

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Dmitrii Mints. 2024-04-13. High order homoclinic tangencies of corank 2. https://arxiv.org/abs/2404.08989

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