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 5 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 $d \ge 5$, 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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [18 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-01392914
Contributor : Sébastien Biebler <>
Submitted on : Saturday, November 5, 2016 - 12:50:39 AM
Last modification on : Thursday, July 18, 2019 - 3:00:04 PM
Long-term archiving on : Monday, February 6, 2017 - 12:11:07 PM

File

biebler-infinity-sinks-C3-4-11...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01392914, version 1

Collections

Citation

Sébastien Biebler. Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^{3}. 2016. ⟨hal-01392914⟩

Share

Metrics

Record views

121

Files downloads

28