2021/08/17 by Sayani Bera, Bera, Sayani, Ratna Pal +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2108.07475
openalex publication_date 2021/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a Hénon map of the form H(x, y) = (y, p(y) - ax), where p is a polynomial of degree at least two and a \not= 0, it is known that the sub-level sets of the Green's function G+H associated with H are Short \mathbb C2's. For a given c > 0, we study the holomorphic automorphism group of such a Short \mathbb C2, namely Ωc = \ G+H < c \. The unbounded domain Ωc ⊂ \mathbb C2 is known to have smooth real analytic Levi-flat boundary. Despite the fact that Ωc admits an exhaustion by biholomorphic images of the unit ball, it turns out that its automorphism group, Aut(Ωc) cannot be too large. On the other hand, examples are provided to show that these automorphism groups are non-trivial in general. We also obtain necessary and sufficient conditions for such a pair of Short \mathbb C2's to be biholomorphic.