An application of the degenerate Beltrami equation: quadratic polynomials with a Siegel disk
نویسندگان
چکیده
منابع مشابه
Mating Siegel Quadratic Polynomials
1.1. Mating: Definitions and some history. Mating quadratic polynomials is a topological construction suggested by Douady and Hubbard [Do2] to partially parametrize quadratic rational maps of the Riemann sphere by pairs of quadratic polynomials. Some results on matings of higher degree maps exist, but we will not discuss them in this paper. While there exist several, presumably equivalent, ways...
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چکیده ندارد.
15 صفحه اولMating a Siegel Disk with the Julia Set of a Real Quadratic Polynomial
In this work, we show that it is possible to construct the mating between a quadratic polynomial with a Siegel disk and a real quadratic polynomial possessing a postcritical orbit that is semi-conjugate to a rigid rotation with the same rotation number as the Siegel disk.
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1.1. In short. — Let p/q be an irreducible fraction (q > 0). Let us define the polynomial P (z) = ez + z. It is well known that the parabolic fixed point z = 0 is the only non repelling periodic point of P , and moreover that it has precisely q repelling petals. The action of P on the (repelling) Écalle-Voronin cylinders is therefore transitive. We will choose one end of these cylinders and cal...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Mathematica
سال: 2018
ISSN: 1239-629X,1798-2383
DOI: 10.5186/aasfm.2018.4311