Slices of the parameter space of cubic polynomials

Slices of the parameter space of cubic polynomials

In this paper, we study slices of the parameter space of cubic polynomials, up to affine conjugacy, given by a fixed value of the multiplier at a non-repelling fixed point. In particular, we study the location of the main cubioid in this parameter space. The main cubioid is the set of affine conjuga...

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Veröffentlicht in:Transactions of the American Mathematical Society 2022-08, Vol.375 (8), p.5313-5359
Hauptverfasser: Blokh, Alexander, Oversteegen, Lex, Timorin, Vladlen
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Oversteegen, Lex
Timorin, Vladlen
description In this paper, we study slices of the parameter space of cubic polynomials, up to affine conjugacy, given by a fixed value of the multiplier at a non-repelling fixed point. In particular, we study the location of the main cubioid in this parameter space. The main cubioid is the set of affine conjugacy classes of complex cubic polynomials that have certain dynamical properties generalizing those of polynomials z^2+c for c in the filled main cardioid.
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