2016/03/30 by Xiaoguang Wang, Wang, Xiaoguang, Yongcheng Yin +1
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN) #math.CV #math.DS #math.GN
paper · pdf · doi:10.48550/arxiv.1603.09309
35 pages, 4 figures
arxiv created 2016/03/30 · arxiv updated 2016/03/31
The hyperbolic components in the moduli space Md of degree d≥2 rational maps are mysterious and fundamental topological objects. For those in the connectedness locus, they are known to be the finite quotients of the Euclidean space ℝ4d-4. In this paper, we study the hyperbolic components in the disconnectedness locus and with minimal complexity: those in the Cantor circle locus. We show that each of them is a finite quotient of the space ℝ4d-4-n×\mathbbTn, where n is determined by the dynamics. The proof relates Riemann surface theory (Abel's Theorem), dynamical system and algebraic topology.