Semigroup-fication of univalent self-maps of the unit disc

从单位圆内的离散迭代到连续全纯函数的半群

Semigroup models for discrete holomorphic iteration in the unit disc

本文提出了一种将单位圆内全纯函数轨道半群化的方法，用于研究轨道收敛速度及非切向收敛行为。

Canonical Models for holomorphic iteration

We construct canonical intertwining semi-models with Kobayashi hyperbolic base space for holomorphic self-maps of complex manifolds which are univalent on some absorbing cocompact hyperbolic domain. In particular, in the unit ball we solve the Valiron equation for hyperbolic univalent self-maps and for hyperbolic semigroups.

Infinitesimal generators of semigroups with prescribed boundary fixed points

We study infinitesimal generators of one-parameter semigroups in the unit disk $\mathbb D$ having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein-Milman Theory we obtain new sharp inequalities relating spectral values at the fixed points with other important quantities having dynamical meaning.vWe also give a new proof of the classical Cowen-Pommerenke inequalities for univalent self-maps of $\mathbb D$.

Parametric representations and boundary fixed points of univalent self-maps of the unit disk

A classical result in the theory of Loewner's parametric representation states that the semigroup $\mathfrak U_*$ of all conformal self-maps $ϕ$ of the unit disk $\mathbb{D}$ normalized by $ϕ(0) = 0$ and $ϕ'(0) > 0$ can be obtained as the reachable set of the Loewner - Kufarev control system $$ \frac{\mathrm{d} w_t}{\mathrm{d} t}=G_t\circ w_t,\quad t\geqslant0,\qquad w_0=\mathsf{id}_{\mathbb{D}}, $$ where the control functions $t\mapsto G_t\in\mathsf{Hol}(\mathbb{D},\mathbb{C})$ form a certain convex cone. Here we extend this result to the semigroup $\mathfrak U[F]$ consisting of all conformal…

非椭圆单叶自映射的中心化子与单位圆盘中的嵌入问题

Centralizers of non-elliptic univalent self-maps and the embeddability problem in the unit disc

本文研究单位圆盘单叶自映射的连续半群嵌入问题，通过分析其中心化子的动力学二分结构，并提出双非椭圆映射同步线性化技术及相关复平面加法子半群。

Boundary distortion estimates for holomorphic maps

We establish some estimates of the the angular derivatives from below for holomorphic self-maps of the unit disk at one and two fixed points of the unit circle provided there is no fixed point inside the unit disk. The results complement Cowen-Pommerenke and Anderson-Vasil'ev type estimates in the case of univalent functions. We use the method of extremal length and propose a new semigroup approach to deriving inequalities for holomorphic self-maps of the disk which are not necessarily univalent using known inequalities for univalent functions. This approach allowed us to receive a new Osserma…