Abstract
We show that there exists a polynomial automorphism f of C3 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≥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 Díaz.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.