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

Published online by Cambridge University Press:  01 June 2018

LIANGANG MA
LIANGANG MA*
Affiliation:
Dept. of Mathematics, Binzhou University, Huanghe 5th road No. 391, Binzhou 256600, Shandong, P. R. China. e-mail: [email protected]
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Abstract

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).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 2 , September 2019 , pp. 369 - 388
Copyright
Copyright © Cambridge Philosophical Society 2018 

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Footnotes

†Supported by 2016Y28 from Binzhou University and ZR2018MF015 from SNSF

References

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