Dynamics of Certain Smooth One-dimensional Mappings I. The C-Denjoy-Koebe distortion lemma

نویسنده

  • Yunping Jiang
چکیده

We prove a technical lemma, the C-Denjoy-Koebe distortion lemma, estimating the distortion of a long composition of a C onedimensional mapping f : M 7→ M with finitely many, non-recurrent, power law critical points. The proof of this lemma combines the ideas of the distortion lemmas of Denjoy and Koebe.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Dynamics of certain non-conformal semigroups

Abstract A semigroup generated by two dimensional C contracting maps is considered. We call a such semigroup regular if the maximum K of the conformal dilatations of generators, the maximum l of the norms of the derivatives of generators and the smoothness α of the generators satisfy a compatibility condition K < 1/l. We prove that the shape of the image of the core of a ball under any element ...

متن کامل

Introduction to Complex Dynamical Systems

An introductory course of lectures is presented on the theory of complex dynamical systems. The main attention is paid to the case of holomorphic mappings of the open unit disk ∆ = {z ∈ C : |z| < 1}. The course starts by presenting detailed information on the simplest holomorphic mappings ∆ → C, which includes the group of homographic maps. Then a description of the theory of holomorphic selfma...

متن کامل

Dynamics of Certain Smooth One-dimensional Mappings II. Geometrically finite one-dimensional mappings

We study geometrically finite one-dimensional mappings. These are a subspace of C one-dimensional mappings with finitely many, critically finite critical points. We study some geometric properties of a mapping in this subspace. We prove that this subspace is closed under quasisymmetrical conjugacy. We also prove that if two mappings in this subspace are topologically conjugate, they are then qu...

متن کامل

The Convenient Setting for Quasianalytic Denjoy–carleman Differentiable Mappings

For quasianalytic Denjoy–Carleman differentiable function classes C where the weight sequence Q = (Qk) is log-convex, stable under derivations, of moderate growth and also an L-intersection (see (1.6)), we prove the following: The category of C-mappings is cartesian closed in the sense that C(E,C(F,G)) ∼= C(E × F,G) for convenient vector spaces. Applications to manifolds of mappings are given: ...

متن کامل

Wandering Domains and Invariant Conformal Structures for Mappings of the 2-torus

A C1 circle diffeomorphism with irrational rotation number need not have any dense orbits. However, any C2 circle diffeomorphism with irrational rotation number must in fact be topologically conjugate to an irrational rotation. This paper addresses the analogous matter for the 2-torus. We say that a diffeomorphism f of T 2, isotopic to the identity, has Denjoy type if hf = Rh, where R is some m...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1990