2021/02/15 by Blokh, Alexander, Oversteegen, Lex, Shepelevtseva, Anastasia +1
#37F20 #37F50 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F45 #Secondary 37F10
paper · doi:10.48550/arxiv.2102.07466
The paper deals with cubic 1-variable polynomials whose Julia sets are connected. Fixing a bounded type rotation number, we obtain a slice of such polynomials with the origin being a fixed Siegel point of the specified rotation number. Such slices as parameter spaces were studied by S. Zakeri, so we call them Zakeri slices. We give a model of the central part of a slice (the subset of the slice that can be approximated by hyperbolic polynomials with Jordan curve Julia sets), and a continuous projection from the central part to the model. The projection is defined dynamically and agrees with the dynamical-analytic parameterization of the Principal Hyperbolic Domain by Petersen and Tan Lei.