Location of Siegel capture polynomials in parameter spaces

نویسندگان

چکیده

A cubic polynomial with a marked fixed point 0 is called an IS-capture if it has Siegel disk D around and contains eventual image of critical point. We show that any on the boundary unique bounded hyperbolic component parameter space determined by rational lamination map relate polynomials to principal domain its closure.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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...

متن کامل

On 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

On Dynamics of Cubic Siegel Polynomials

Let f be a polynomial of degree d ≥ 2 in the complex plane and consider the following statements: (A d) " If f has a fixed Siegel disk ∆ of bounded type rotation number, then ∂∆ is a quasicircle passing through some critical point of f. " (B d) " If f has a fixed Siegel disk ∆ such that ∂∆ is a quasicircle passing through some critical point of f , then the rotation number of ∆ is bounded type....

متن کامل

Hilbert-Siegel moduli spaces in positive characteristic

Hilbert-Siegel varieties are moduli spaces for abelian varieties equipped with an action by an order OK in a fixed, totally real field K. As such, they include both the Siegel moduli spaces (use K = Q and the action is the standard one) and Hilbert-Blumenthal varieties (where the dimension of K is the same as that of the abelian varieties in question). In this paper we study certain phenomena a...

متن کامل

Finite Group Actions on Siegel Modular Spaces

The theory of nonabelian cohomology is used to show that the set of fixed points of a finite group acting on a Siegel modular space is a union of Shimura varieties

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Nonlinearity

سال: 2021

ISSN: ['0951-7715', '1361-6544']

DOI: https://doi.org/10.1088/1361-6544/abb9f9