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arXiv · 1209.1753

Multicorns are not Path Connected

John Hubbard·Dierk Schleicher
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Abstract

The "multicorn" is the connectedness locus of unicritical antiholomorphic polynomials $z\mapsto \bar r{z}^d+c$; the special case $d=2$ was named "tricorn" by Milnor. It appears as a natural local configuration in spaces of real cubic polynomials. We prove that no multicorn for $d\ge 2$ is pathwise connected, confirming a classical prediction based on numerical observations.

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John Hubbard, Dierk Schleicher. 2012-09-08. Multicorns are not Path Connected. https://arxiv.org/abs/1209.1753

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