相关论文: Dynamics in the complex bidisc

We define a class of smashing localisations which we call compactly central, and classify compactly central localisations of $Sp_{(p)}$ and of $Sp$. Our main result is that $L_n^f$ is a compactly central localisation. A map $\alpha: 1 \to…

An w-limit set of a continuous self-mapping of a compact metric space X is said to be totally periodic if all of its points are periodic. We say that X has the w-FTP property provided that for each continuous self-mapping f of X, every…

Let $\Omega$ be a complex lattice which does not have complex multiplication and $\wp=\wp_\Omega$ the Weierstrass $\wp$-function associated to it. Let $D\subseteq\mathbb{C}$ be a disc and $I\subseteq\mathbb{R}$ be a bounded closed interval…

Let $f$ be a holomorphic function on the strip $\{z\in C: -\alpha<Im z<\alpha\}, \alpha > 0$, belonging to the class $H(\alpha,-\alpha;\epsilon)$ defined below. It is shown that there exist holomorphic functions $w_1$ on $\{z\in C: 0<Im z…

A $1$-Lipschitz map $f$ from a convex compact set to itself has fixed points. This consequence of Brouwer's or Schauder's fixed point theorem has more elementary proofs by approximating $f$ by $\lambda$-contractions, $f_\lambda$. We study…

We give an example of a parabolic holomorphic self-map $f$ of the unit ball $\mathbb B^2\subset \mathbb C^2$ whose canonical Kobayashi hyperbolic semi-model is given by an elliptic automorphism of the disc $\mathbb D\subset \mathbb C$,…

For a K\"{a}hler manifold endowed with a weighted measure $e^{-f}\,dv,$ the associated weighted Hodge Laplacian $\Delta _{f}$ maps the space of $(p,q)$-forms to itself if and only if the $(1,0)$-part of the gradient vector field $\nabla f$…

The classical Lefschetz fixed point theorem states that the number of fixed points, counted with multiplicity $\pm 1$, of a smooth map $f$ from a manifold $M$ to itself can be calculated as the alternating sum $\sum (-1)^k \textrm{ tr }…

The valence of a function $f$ at a point $w$ is the number of distinct, finite solutions to $f(z) = w$. Let $f$ be a complex-valued harmonic function in an open set $R \subseteq \mathbb{C}$. Let $S$ denote the critical set of $f$ and $C(f)$…

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt's theorem: every holomorphic…

Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f…

We consider polynomial maps $f:\C\to\C$ of degree $d\ge 2$, or more generally polynomial maps from a finite union of copies of $\C$ to itself which have degree two or more on each copy. In any space $\p^{S}$ of suitably normalized maps of…

In this article, we consider a bounded pseudoconvex domain in ${\bf C}^2$ satifying: (a) it admits a proper holomorphic mapping $f$ onto the unit ball $B^2$, and (b) it is simply connected and has a real analytic boundary. According to…

In this paper we give some quantative characteristics of boundary asymptotic behavior of semigroups of holomorphic self-mappings of the unit disk including the limit curvature of their trajectories at the boundary Denjoy--Wolff point. This…

We prove the existence and the essential uniqueness of canonical models for the forward (resp. backward) iteration of a holomorphic self-map $f$ of a cocompact Kobayashi hyperbolic complex manifold, such as the ball $\mathbb{B}^q$ or the…

Let $f:M\rightarrow M$ be a biholomorphisms on two--dimensional a complex manifold, and let $X\subseteq M$ be a compact $f$--invariant set such that $f|X$ is asymptotically dissipative and without sinks periodic points. We introduce a…

Given linearly independent holomorphic functions $f_0,...,f_n$ on a planar domain $\Omega$, let $\mathcal E$ be the set of those points $z\in\Omega$ where a nontrivial linear combination $\sum_{j=0}^n\lambda_jf_j$ may have a zero of…

Let $\Gamma_n$, $n \geq 2$, denote the symmetrized polydisc in $\mathbb{C}^n$, and $\Gamma_1$ be the closed unit disc in $\mathbb{C}$. We provide some characterizations of elements in $\Gamma_n$. In particular, an element $(s_1, \ldots,…

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…

We prove that a proper holomorphic map on the unit disk in the complex plane is uniquely determined up to post-composition with a Moebius transformation by its critical points.