Non-landing parameter rays of the multicorns

• 成果类型: Article
• 署名作者: Inou, Hiroyuki; Mukherjee, Sabyasachi
• 署名单位: Kyoto University; Constructor University; State University of New York (SUNY) System; Stony Brook University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0627-3
• 发表日期: 2016
• 页码: 869-893
• 关键词: cubic polynomials; points; MAPS

摘要

It is well known that every rational parameter ray of the Mandelbrot set lands at a single parameter. We study the rational parameter rays of the multicorn , the connectedness locus of unicritical antiholomorphic polynomials of degree d, and give a complete description of their accumulation properties. One of the principal results is that the parameter rays accumulating on the boundaries of odd period (except period 1) hyperbolic components of the multicorns do not land, but accumulate on arcs of positive length consisting of parabolic parameters. We also show the existence of undecorated real-analytic arcs on the boundaries of the multicorns, which implies that the centers of hyperbolic components do not accumulate on the entire boundary of , and the Misiurewicz parameters are not dense on the boundary of .