Rational maps without Herman rings
نویسندگان
چکیده
منابع مشابه
The Fine Structure of Herman Rings
We study the geometric structure of the boundary of Herman rings in a model family of Blaschke products of degree 3. Shishikura’s quasiconformal surgery relates the Herman ring to the Siegel disk of a quadratic polynomial. By studying the regularity properties of the maps involved, we can transfer McMullen’s results on the fine local geometry of Siegel disks to the Herman ring setting.
متن کاملA Decomposition Theorem for Herman Maps
In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed ‘Herman map’ is developed. It’s shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations an...
متن کاملClassification on Herman Rings of Extended Blaschke Equations
This paper presents some interesting results of numerical analysis of the Extended Blaschke functions, which are constructed by extending Blaschke product. On the complex plane, the convergent domains of the functions form fractal patterns of constrained Herman rings with limited-layered structures, which demonstrate skip-symmetry, symmetry broken, chaos, and degeneracy in conjunction with para...
متن کاملOn the Configuration of Herman Rings of Meromorphic Functions
We prove some results concerning the possible configurations of Herman rings for transcendental meromorphic functions. We show that one pole is enough to obtain cycles of Herman rings of arbitrary period and give a sufficient condition for a configuration to be realizable.
متن کاملF-rational Rings Have Rational Singularities
It is proved that an excellent local ring of prime characteristic in which a single ideal generated by any system of parameters is tightly closed must be pseu-dorational. A key point in the proof is a characterization of F-rational local rings as those Cohen-Macaulay local rings (R; m) in which the local cohomology module H d m (R) (where d is the dimension of R) have no submodules stable under...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13336