Symmetries of the Julia sets of König's methods for polynomials

• DOI: 10.1016/j.jmaa.2015.06.066
• Publication Date: 2015-07-04T17:55:55Z
• Authors: Gang Liu; Junyang Gao
• Keywords: Julia set; Newton fractal

Abstract Let Σ ( R ) be the group of symmetries of the Julia set of a rational map R and K f , n be the Konig's method for polynomial f of order n ( ≥ 2 ) . For any given integer n ≥ 2 , we prove that if f is in normal form, then Σ ( f ) is a subgroup of Σ ( K f , n ) . We also obtain a necessary and sufficient condition for the Julia set of K f , n to be a line.