Related papers: Rotation domains and Stable Baker omitted value

Let f be a real entire function whose set S(f) of singular values is real and bounded. We show that, if f satisfies a certain function-theoretic condition (the "sector condition"), then $f$ has no wandering domains. Our result includes all…

We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main…

We review recent theoretical progress in understanding spatially uniform $s$-wave superconductivity which arises from a fermion-fermion interaction, which is repulsive on the Matsubara axis, where it is real, but does depend on the…

Let f be a transcendental meromorphic function. Suppose that the finite part of the postsingular set of f is bounded, that f has no recurrent critical points or wandering domains, and that the degree of pre-poles of f is uniformly bounded.…

We present an analysis of the Aharonov-Bohm oscillations for a mesoscopic ring with a quantum dot inserted in one of its arms. It is shown that microreversibility demands that the phase of the Aharonov-Bohm oscillations changes {\it…

We show the direct applicability of the Brouwer fixed point theorem for the existence of equilibrium points and periodic solutions for differential systems on general domains satisfying geometric conditions at the boundary. We develop a…

We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for…

We investigate the relation between Bell function values (BFV) of the reduced density matrix and the topological quantum phase transitions in the Kitaev-Castelnovo-Chamon model. % [Phys. Rev. B \textbf{77}, %054433 (2008)]. We find that the…

Let T be a finite subset of the complex unit circle S^1, and define f: S^1 -> S^1 by f(z) = z^d. Let CH(T) denote the convex hull of T. If card(T) = N > 2, then CH(T) defines a polygon with N sides. The N-gon CH(T) is called a…

By adapting the near-degenerate regime designed by Kahn, Lyubich, and D. Dudko, we prove that the boundaries of Herman rings with bounded type rotation number and of the simplest configuration are quasicircles with dilatation depending only…

This paper consists of tow parts. One is to study the existence of a point $a$ in the intersection of Julia set and escaping set such that $\arg z=\theta$ is a singular direction if $\theta$ is a limit point of $\{\arg f^n(a)\}$ under some…

The classical Gauss--Lucas theorem describes the location of the critical points of a polynomial. There is also a hyperbolic version, due to Walsh, in which the role of polynomials is played by finite Blaschke products on the unit disk. We…

Wandering Fatou components were recently constructed by Astorg et al for higher-dimensional holomorphic maps on projective spaces. Their examples are polynomial skew products with a parabolic invariant line. In this paper, we study this…

Let f be a degree d polynomial defined over the nonarchimedean field C_p, normalized so f is monic and f(0)=0. We say f is post-critically bounded, or PCB, if all of its critical points have bounded orbit under iteration of f. It is known…

We consider 2+1--dimensional analogues of the Bertotti-Robinson (BR) spacetimes in the sense that the coefficient at the angular part is a constant. We show that such BR-like solutions are either pure static or uncharged rotating. We trace…

$R_+^{n\times n}$ denotes the set of $n\times n$ non-negative matrices. For $A\in R_+^{n\times n}$ let $\Omega(A)$ be the set of all matrices that can be formed by permuting the elements within each row of $A$. Formally: $$\Omega(A)=\{B\in…

We study the existence of solutions of mixed Riemann-Hilbert or Cherepanov boundary value problem with simply connected fibers on the unit disk ${\Delta}$. Let $L$ be a closed arc on $\partial{\Delta}$ with the end points $\omega_{-1},…

Rudin's version of the classical Julia-Wolff-Carath\'eodory theorem is a cornerstone of holomorphic function theory in the unit ball of $\mathbb{C}^d$. In this paper we obtain a complete generalization of Rudin's theorem for a holomorphic…

We obtain an essential spectral gap for a convex co-compact hyperbolic surface $M=\Gamma\backslash\mathbb H^2$ which depends only on the dimension $\delta$ of the limit set. More precisely, we show that when $\delta>0$ there exists…

This paper treats a holomorphic self-mapping f: Omega --> Omega of a bounded domain Omega in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinite-dimensional version of the…