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

  • LIANGANG MA (a1)

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, cM 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).

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

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

  • LIANGANG MA (a1)

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