Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3} - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Advances in Mathematics Année : 2020

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

Résumé

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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Dates et versions

hal-01392917 , version 1 (07-11-2016)
hal-01392917 , version 2 (07-05-2018)
hal-01392917 , version 3 (10-12-2019)

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Citer

Sébastien Biebler. Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3}. Advances in Mathematics, 2020, 361, pp.106952. ⟨10.1016/j.aim.2019.106952⟩. ⟨hal-01392917v3⟩
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