2024/01/30 by Beltrami, Veronica
#37F80 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2401.16903
We study the stable dynamics of non-polynomial automorphisms of ℂ2 of the form F(z,w)=(e-zm+ δe(2 π)/(m)i w , z), with m≥ 2 a natural number and ℝ\niδ>2. If m is even, there are (m)/(2) cycles of escaping Fatou components, all of period 2m. If m is odd there are (m-1)/(2) cycles of escaping Fatou components of period 2m and just one cycle of escaping Fatou components of period m. These maps have two distinct limit functions on each cycle, both of which have generic rank 1. Each Fatou component in each cycle has two disjoint and hyperbolic limit sets on the line at infinity, except for the Fatou components that belong to the unique cycle of period m: the latter in fact have the same hyperbolic limit set on the line at infinity.