2023/04/19 by Kohei Ueno, Ueno, Kohei
Mathematics · Physics and Astronomy · #32H50 (Primary) #37F80 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2304.09457
openalex publication_date 2023/04/19 · openalex created_date 2023/04/24 · openalex updated_date 2026/07/28
We study the dynamics of a superattracting skew product f on the attracting basin. As the first strategy, we find out forward f-invariant wedge-shaped regions in the basin, on some of which f is conjugate to monomial maps, and consider whether the unions of all the preimages of the regions coincide with the basin. As the second strategy, we show the existence and properties of several kinds of plurisubharmonic functions of f, the main functions of which are induced from the Böttcher coordinates, and investigate the asymptotic behavior of the functions toward the boundaries of the unions. Consequently, we obtain a plurisubharmonic function on the complement of specific fibers in the basin, which is continuous and pluriharmonic on open and dense subsets of the complement and describes an certain weighted vertical dynamics well.