Robust complex heterodimensional cycles
Dynamical Systems
2025-01-15 v1
Abstract
A diffeomorphism f has a heterodimensional cycle if it displays two (transitive) hyperbolic sets K and K' with different indices such that the unstable set of K intersects the stable one of K' and vice versa. We prove that it is possible to find robust heterodimensional cycles for families of polynomial automorphisms of C^3 . The proof is based on Bonatti-D{\'i}az blenders.
Cite
@article{arxiv.2501.07950,
title = {Robust complex heterodimensional cycles},
author = {Sébastien Biebler},
journal= {arXiv preprint arXiv:2501.07950},
year = {2025}
}