• Corpus ID: 16201760

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

@article{Biebler2016PersistentHT,
  title={Persistent homoclinic tangencies and infinitely many sinks for residual sets of automorphisms of low degree in C^\{3\}},
  author={S'ebastien Biebler},
  journal={arXiv: Dynamical Systems},
  year={2016}
}
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… 
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