Robust complex heterodimensional cycles

TL;DR

This paper demonstrates the existence of robust heterodimensional cycles in polynomial automorphisms of C^3, using Bonatti-Díaz blenders to establish their robustness in dynamical systems.

Contribution

It introduces the first construction of robust heterodimensional cycles in polynomial automorphisms of complex three-dimensional space.

Findings

Robust heterodimensional cycles are achievable in polynomial automorphisms of C^3.

The proof utilizes Bonatti-Díaz blenders to ensure robustness.

The work extends the understanding of complex dynamical systems with heterodimensional cycles.

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.