Modeling Core Parts of Zakeri Slices I

Blokh, Alexander; Oversteegen, Lex G.; Shepelevtseva, Anastasia; Timorin, Vladlen

doi:10.17323/1609-4514-2022-22-2-265-294

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…On the other hand, the structure of the neutral slices F λ with |λ| = 1 is much more delicate. There are still many unanswered questions about them (cf [11]); see [10,48,49] for very recent results concerning the simplest neutral slices(where λ = e 2π iθ , with θ being rational or irrational of bounded type). An earlier paper [44] studies the dynamics of polynomials from F 1 .…”

Section: Applications and Further Directionsmentioning

confidence: 99%

Upper bounds for the moduli of polynomial-like maps

Blokh,

Oversteegen,

Timorin

2024

Nonlinearity

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We establish a version of the Pommerenke–Levin–Yoccoz inequality for the modulus of a polynomial-like (PL) restriction of a polynomial and give two applications. First we show that if the modulus of a PL restriction of a polynomial is bounded from below then this restricts the combinatorics of the polynomial. The second application concerns parameter slices of cubic polynomials given by the non-repelling multiplier of a fixed point. Namely, the intersection of the so-called Main Cubioid and the multiplier slice lies in the closure of the principal hyperbolic domain, with possible exception of queer components.

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Section: Applications and Further Directionsmentioning

confidence: 99%

Upper bounds for the moduli of polynomial-like maps

Blokh,

Oversteegen,

Timorin

2024

Nonlinearity

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“…Bottom right: λ = e πi √ 2 ; the set P λ looks like K(λz + z 2 ), in which the central Fatou component is replaced with a simple arc (Zakeri curve, cf. [Z99] and[BOST22]).…”

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confidence: 99%

Slices of the parameter space of cubic polynomials

Blokh

Oversteegen²,

Timorin

2022

Trans. Amer. Math. Soc.

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We construct a locally connected model of the boundary of the cubic connectedness locus. The model is obtained by constructing a decomposition of the space of critical portraits and collapsing elements of the decomposition into points. This model is similar to a quotient of the quadratic combinatorial locus where all baby Mandelbrot sets are collapsed to points. All fibers of the model, possibly except one, are connected.

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Modeling Core Parts of Zakeri Slices I

Cited by 2 publications

References 20 publications

Upper bounds for the moduli of polynomial-like maps

Upper bounds for the moduli of polynomial-like maps

Slices of the parameter space of cubic polynomials

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