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Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3}

Abstract : We show that there exists a polynomial automorphism $f$ of $\mathbb{C}^{3}$ of degree 2 such that for every automorphism $g$ sufficiently close to $f$, $g$ admits a tangency between the stable and unstable laminations of some hyperbolic set. As a consequence, for each $d \ge 2$, there exists an open set of polynomial automorphisms of degree at most $d$ in which the automorphisms having infinitely many sinks are dense. To prove these results, we give a complex analogous to the notion of blender introduced by Bonatti and Diaz.
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https://hal-upec-upem.archives-ouvertes.fr/hal-01392917
Contributor : Sébastien Biebler <>
Submitted on : Tuesday, December 10, 2019 - 12:45:49 AM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM
Long-term archiving on: : Wednesday, March 11, 2020 - 1:51:15 PM

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  • HAL Id : hal-01392917, version 3
  • ARXIV : 1611.02011

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Sébastien Biebler. Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3}. 2018. ⟨hal-01392917v3⟩

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