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arXiv · 2010.01129

Discontinuity of straightening in anti-holomorphic dynamics: II

Hiroyuki Inou·Sabyasachi Mukherjee
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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.

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Hiroyuki Inou, Sabyasachi Mukherjee. 2020-10-02. Discontinuity of straightening in anti-holomorphic dynamics: II. https://doi.org/10.1093/imrn%2Frnaa365

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