相关论文: Invariant curves and semiconjugacies of rational f…

We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.

In this paper we prove an asymptotically sharp Bernstein-type inequality for polynomials on analytic Jordan arcs. Also a general statement on mapping of a domain bounded by finitely many Jordan curves onto a complement to a system of the…

We investigate semiconjugate rational functions, that is rational functions $A,$ $B$ related by the functional equation $A\circ X=X\circ B$, where $X$ is a rational function of degree at least two. We show that if $A$ and $B$ is a pair of…

We characterize the space of restrictions of real rational functions to certain algebraic Jordan curves in the plane via the Dirichlet-to-Neumann map associated to the domain in the complex plane bounded by the curve and its Bergman kernel.…

The dynamics of all quadratic Newton maps of rational functions are completely described. The Julia set of such a map is found to be either a Jordan curve or totally disconnected. It is proved that no Newton map with degree at least three…

The aim of this article is to start a study of Jordan derivations in finite endomorphism semirings.

We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of…

The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn…

New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…

Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…

Invariant functions and metrics are studied on various classes of domains in $\Bbb C^n.$

The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the other analytic in the unbounded complementary component of…

We present a construction of new invariant sets for fibred polynomial dynamics with base an irrational rotation over the unit circle, called multi-curves. Furthermore, the local dynamical theory for attracting invariant curves is extended…

We show that both, the Jordan curve theorem and the Schoenflies theorem extend to non-metric manifolds (at least in the two-dimensional context), and conclude by some dynamical applications \`a la Poincar\'e-Bendixson.

We establish a general result on the existence of partially defined semiconjugacies between rational functions acting on the Riemann sphere. The semiconjugacies are defined on the complements to at most one-dimensional sets. They are…

In this thesis new objects to the existing set of invariants of Lie algebras are added. These invariant characteristics are capable of describing the nilpotent parametric continuum of Lie algebras. The properties of these invariants, in…

We study the variety of complex $n$-dimensional Jordan algebras using techniques from Geometric Invariant Theory.

Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational…

The study of the number of photons leads to a new way of characterizing curves and to a novel integral invariant over curves.

Adopting the approach of [7] we study rational function carrying invariant line fields on the Julia set. In particular, we show that under certain weak conditions all possible measurable invariant line fields of a rational function on its…