Nevanlinna, Siegel, and Cremer
نویسنده
چکیده
We study an irrationally indifferent cycle of points or circles of a rational function, which is either Siegel or Cremer by definition. We invent a new argument from the viewpoint of the Nevanlinna theory. Using this argument, we give a clear interpretation of some Diophantine quantity associated with an irrationally indifferent cycle. This quantity turns out to be Nevanlinnatheoretical. As a consequence, we show that an irrationally indifferent cycle is Cremer if this Nevanlinna-theoretical quantity does not vanish.
منابع مشابه
Biaccessiblility in Quadratic Julia Sets Ii the Siegel and Cremer Cases
Let f be a quadratic polynomial which has an irrationally indi erent xed point Let z be a biaccessible point in the Julia set of f Then In the Siegel case the orbit of z must eventually hit the critical point of f In the Cremer case the orbit of z must eventually hit the xed point Siegel polynomials with biaccessible critical point certainly exist but in the Cremer case it is possible that biac...
متن کامل2 Xavier Buff And
We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure in three cases: the presence of a Cremer fixed point, the presence of a Siegel disk, the presence of infinitely many (satellite) renormalizations.
متن کاملXavier Buff and Arnaud Chéritat
We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure. We find such examples with a Cremer fixed point, with a Siegel disk, or with infinitely many satellite renormalizations.
متن کاملSingularities of Schröder Maps and Unhyperbolicity of Rational Functions
We study transcendental singularities of a Schröder map arising from a rational function f , using results from complex dynamics and Nevanlinna theory. These maps are transcendental meromorphic functions of finite order in the complex plane. We show that their transcendental singularities lie over the set where f is not semihyperbolic (unhyperbolic). In addition, if they are direct, then they l...
متن کاملOn Atkin-Lehner correspondences on Siegel spaces
We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of $GSp(2g)$. Old Siegel forms are induced by geometric correspondences on Siegel moduli spaces which commute with almost all local Hecke algebras. We also introduce an algorithm to get equations for moduli spaces of Siegel-Parahoric level structures, once we have equations for prime l...
متن کامل