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arXiv · 1907.01089

Robust degenerate unfoldings of cycles and tangencies

Pablo G. Barrientos·Artem Raibekas
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Abstract

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 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.

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Pablo G. Barrientos, Artem Raibekas. 2019-07-01. Robust degenerate unfoldings of cycles and tangencies. https://doi.org/10.1007/s10884-020-09857-0

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