English

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