2025/02/27 by Muhan Luo, Qi Zhou, Luo, Muhan +1 · 1 citation
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2502.20103
openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that under the natural assumption over the dynamical degrees, the saddle periodic points of a Hénon-like map in any dimension equidistribute with respect to the equilibrium measure. Our work is a generalization of results of Bedford-Lyubich-Smillie, Dujardin and Dinh-Sibony along with improvements of their techniques. We also investigate some fine properties of Green currents associated with the map. On the pluripotential-theory side, in our non-compact setting, the wedge product of two positive closed currents of complementary bi-degrees can be defined using super-potentials and the density theory. We prove that these two definitions are coherent.