A continuity result on quadratic matings with respect to parameters of odd denominator rationals

Autor:	Liangang Ma
Rok vydání:	2018
Předmět:	Combinatorics Rational number Quadratic equation General Mathematics Bounded function Hyperbolic polynomial Component (group theory) Center (group theory) Lamination (topology) Mandelbrot set Mathematics
Zdroj:	Mathematical Proceedings of the Cambridge Philosophical Society. 167:369-388
ISSN:	1469-8064 0305-0041
DOI:	10.1017/s0305004118000397
Popis:	In this paper we prove a continuity result on matings of quadratic lamination maps sp depending on odd denominator rationals p ∈(0,1). One of the two mating components is fixed in the result. Note that our result has its implication on continuity of matings of quadratic hyperbolic polynomials fc(z)=z2 + c, c ∈ M the Mandelbrot set with respect to the usual parameters c. This is because every quadratic hyperbolic polynomial in M is contained in a bounded hyperbolic component. Its center is Thurston equivalent to some quadratic lamination map sp, and there are bounds on sizes of limbs of M and on sizes of limbs of the mating components on the quadratic parameter slice Perm′(0).
Databáze:	OpenAIRE
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