Topological and geometric hyperbolicity criteria for polynomial automorphisms of C²

2020/06/03 by Eric Bedford, Romain Dujardin, Bedford, Eric +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CV #math.DS

paper · pdf · doi:10.48550/arxiv.2006.02088

arxiv created 2020/06/03 · openalex publication_date 2020/06/03 · arxiv updated 2020/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that uniform hyperbolicity is invariant under topological conjugacy for dissipative polynomial automorphisms of C². Along the way we also show that a sufficient condition for hyperbolicity is that local stable and unstable manifolds of saddle points have uniform geometry.

Citations

• Structure of partially hyperbolic Hénon maps

Related

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• Hyperbolicity and Quasi-hyperbolicity in Polynomial Diffeomorphisms of \Bbb C²
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• Polynomial Diffeomorphisms of \C². VIII: Quasi-Expansion