Robust complex heterodimensional cycles

2025/01/14 by Sébastien Biebler, Biebler, Sébastien
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2501.07950

openalex publication_date 2025/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 C³ . The proof is based on Bonatti-Díaz blenders.

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