Displaying similar documents to “The multiplicity of the Lyashko-Looijenga mapping on the discriminant strata of even and odd polynomials”

A polynomial with 2k critical values at infinity

Janusz Gwoździewicz, Maciej Sękalski (2004)

Annales Polonici Mathematici

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We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.

Iterations of rational functions: which hyperbolic components contain polynomials?

Feliks Przytycki (1996)

Fundamenta Mathematicae

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Let H d be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if f ∈ H d and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of H d containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate...

Critical portraits for postcritically finite polynomials

Alfredo Poirier (2009)

Fundamenta Mathematicae

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We extend the work of Bielefeld, Fisher and Hubbard on critical portraits to arbitrary postcritically finite polynomials. This gives the classification of such polynomials as dynamical systems in terms of their external ray behavior.

The Connectivity Of Domination Dot-Critical Graphs With No Critical Vertices

Michitaka Furuya (2014)

Discussiones Mathematicae Graph Theory

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An edge of a graph is called dot-critical if its contraction decreases the domination number. A graph is said to be dot-critical if all of its edges are dot-critical. A vertex of a graph is called critical if its deletion decreases the domination number. In A note on the domination dot-critical graphs, Discrete Appl. Math. 157 (2009) 3743-3745, Chen and Shiu constructed for each even integer k ≥ 4 infinitely many k-dot-critical graphs G with no critical vertices and k(G) = 1. In this...