2021/02/10 by Leandro Arosio, Arosio, Leandro, Anna Miriam Benini +5
Mathematics · Physics and Astronomy · #37F80 #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
paper · pdf · doi:10.48550/arxiv.2102.05479
openalex publication_date 2021/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental Hénon maps offers the potential of combining ideas from transcendental dynamics in one variable, and the dynamics of polynomial Hénon maps in two. Here we show that these maps all have infinite topological and measure theoretic entropy. The proof also implies the existence of infinitely many periodic orbits of any order greater than two.