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Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of quadratic Julia sets

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  • We prove that for any infinite collection of quadratic Julia sets, there exists a transcendental entire function whose Julia set contains quasiconformal copies of the given quadratic Julia sets. In order to prove the result, we construct a quasiregular map with required dynamics and employ the quasiconformal surgery to obtain the desired transcendental entire function. In addition, the transcendental entire function has order zero.

    Mathematics Subject Classification: Primary: 37F10; Secondary: 30D05, 37F50.


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  • Figure 1.  The definition of the quasiregular map g near infinity

    Figure 2.  The definition of the quasiregular map $ g $ near $ R_{m(j)} $

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