Discontinuity of straightening in anti-holomorphic dynamics: II
Dynamical Systems
2022-04-26 v2 Complex Variables
Abstract
In [M3], Milnor found Tricorn-like sets in the parameter space of real cubic polynomials. We give a rigorous definition of these Tricorn-like sets as suitable renormalization loci, and show that the dynamically natural straightening map from such a Tricorn-like set to the original Tricorn is discontinuous. We also prove some rigidity theorems for polynomial parabolic germs, which state that one can recover unicritical holomorphic and anti-holomorphic polynomials from their parabolic germs.
Keywords
Cite
@article{arxiv.2010.01129,
title = {Discontinuity of straightening in anti-holomorphic dynamics: II},
author = {Hiroyuki Inou and Sabyasachi Mukherjee},
journal= {arXiv preprint arXiv:2010.01129},
year = {2022}
}
Comments
Same as published version. Part I is available at arXiv:1605.08061v5