Baker Domains and Singularities for Certain Meromorphic Functions

Letfbeanon-linearmeromorphicfunctiondefinedinthecomplexplaneC.TheFatousetF(f)offisthelargestsubsetofCwheretheiteratesfoffformanormalfamily.ThecomplementofF(f)iscalledtheJuliasetanddenotedbyJ(f).IfUisacomponentofF(f),thenf(U)iscontainedinsomecomponentofF(f)whichwedenotebyUn.IfUnnUrn=.foralln/m,thenUiscalledwandering.OtherwiseUiscalledeventuallyperiodic.Inparticular,ifUk=UforsomepENandUrn/Ufor0Sm相似文献   

多连通域之间的共形映射及其Schwarz导数

证明了扩充复平面C的多连通子区域之间的共形映射的一个分解定理,并利用此定理给出了定义在C的多连通子区域内的单叶全纯函数的双曲上确界范数的一致有界性的一个简单证明.     

Finite Element Approximation of Conformal Mappings to Unbounded Jordan Domains

In two-dimensional Euclidean space, a simply connected unbounded domain whose boundary is a Jordan curve is called an unbounded Jordan domain. In this article, we discuss a piecewise linear finite element approximation of conformal mappings from the unit disk of the plane to unbounded Jordan domains. Some convergence results and error analysis are presented. Numerical examples are also given.     

An Orthonormalization Method for the Approximate Conformal Mapping of Multiply-Connected Domains

We consider the use of an orthonormalization method for constructingapproximations to one of the standard conformal maps for multiply-connecteddomains. The method has been used successfully in [12], butonly for the mapping of doubly-connected domains. Our purposehere is to consider its application to the mapping of domainswhose connectivity is greater than two.     

Conjugacies and invariant manifolds via evolution semigroups

For a linear evolution family with a nonuniformly hyperbolic behavior, we give simple proofs of the existence of topological conjugacies and stable invariant manifolds under sufficiently small perturbations. The proofs are obtained via evolution semigroups, which allows us to pass from the original nonautonomous nonuni-formly hyperbolic dynamics to one that is autonomous and uniformly hyperbolic.     

Reversibility of Conjugacies for Nonautonomous Equations

We establish a reversible version of the Grobman–Hartman theorem for nonautonomous differential equations in Banach spaces. Namely, we show that if the differential equation is reversible, then the topological conjugacies in the Grobman–Hartman theorem also commute with the symmetries. The result is illustrated with an example.     

The Bergman Kernel Method for the Numerical Conformal Mapping of Simply Connected Domains

A numerical method for the conformal mapping of simply-connecteddomains onto the unit disc is considered. The method is basedon the use of the Bergman kernel function of the domain. Itis shown that, for a successful application, the basis of theseries representation of the kernel must include terms thatreflect the main singular behaviour of the kernel in the complementof the domain.     

有界多连通区域数值保角变换的GMRES(m)法北大核心CSCD

求解复杂多连通区域的保角变换函数是困难的.针对这一问题,该文将求解保角变换函数转化为利用模拟电荷法求解一对定义在问题区域上的共轭调和函数,再根据边界条件建立约束方程,并利用GMRES(m)(the generalized minimal residual method)算法求解约束方程,获得了模拟电荷,进而构造了高精度的近似保角变换函数,将有界多连通区域映射为三种无界正则狭缝域.数值实验验证了该文算法的有效性.     

On the Problem of Maximizing the Product of Powers of Conformal Radii Nonoverlapping Domains

A sharp estimate of the product

Conjugacies between rational maps and extremal quasiconformal maps

We show that two rational maps which are -quasiconformally combinatorially equivalent are -quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy.

     

Conjugacies for linear and nonlinear perturbations of nonuniform behavior

We construct topological conjugacies between linear and nonlinear evolution operators that admit either a nonuniform exponential contraction or a nonuniform exponential dichotomy. We consider evolution operators defined by nonautonomous differential equations x^′=A(t)x+f(t,x) in a Banach space. The conjugacies are obtained by first considering sufficiently small linear and nonlinear perturbations of linear equations x^′=A(t)x. In the case of linear perturbations, we construct in a more or less explicit manner topological conjugacies between the two linear flows. In the case of nonlinear perturbations, we obtain a version of the Grobman-Hartman theorem for nonuniformly hyperbolic dynamics. Furthermore, all the conjugacies that we construct are locally Hölder continuous provided that the vectors fields are of class C¹. As a byproduct of our approach, we give conditions for the robustness of strong nonuniform exponential behavior, in the sense that under sufficiently small perturbations the structure determined by the stable and unstable bundles persists up to small variations. We also show that the constants determining the nonuniform exponential contraction or nonuniform exponential dichotomy vary continuously with the perturbation. All the results are obtained in Banach spaces.     

超连续Domain与拟超连续Domian

讨论了超连续domain与拟超连续domain的相关性质,证明了超连续半格范畴为有性质M*的拟超连续domain范畴的反射子范畴。     

Lip_J-扩张域和一致域(英文)

本文证明了如下两个结果:(1)域D(?)R~n是一致域当且仅当D是Lip_J-扩张域;(2)Jordan域D(?)R~2是拟圆当且仅当对在D上满足|f′(z)|≤d(z,(?)D)~(-1)的任意的解析函数f恒有f∈Lip_J(D),其中J(x_1,x_2)=1/2 log(1+|x_1-x_2|/d(x_1,(?)D))(1+|x_1-x_2|/d(x_2,(?)D)),x_1,x_2∈D.     

Surfaces in Conformal Geometry

Properties of submanifolds are examined which remain invariantunder a conformal change of metric of the ambiant space. In particular,the Willmore energy functional is discussed as is the Willmoreconjecture for tori.     

Conformal autosimilarity

We prove that the conformally autosimilar closed subsets of the Euclidean sphere are exactly the limit sets of convex cocompact Kleinian groups. We also prove other similar results.