Related papers: Singularities of inverse functions
The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
The plenary presentations of the conference are summarised, highlighting some aspects that were of particular interest and attempting to link a few of the topics covered. Particular emphasis is placed on the problem of deep-inelastic…
Lecture 1 provides an introduction to dynamical electroweak symmetry breaking. Lectures 2 and 3 give an introduction to compositeness, with emphasis on effective lagrangians, power-counting, and the 't Hooft anomaly-matching conditions.
In the main part of the paper, on the basis of contour integration of complex meromorphic functions whose singularities lie onto an integration contour, in the first step, a concept of improper integrals absolute existence of meromorphic…
We give a short survey on generalizations of Nevanlinna's theorems on zero distribution of bounded holomorphic functions and representation of meromorphic functions in multiply connected domains. It is a part of our report in the conference…
In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.
We show that if a meromorphic function has a direct singularity over infinity, then the escaping set has an unbounded component and the intersection of the escaping set with the Julia set contains continua. This intersection has an…
Let $D_j\subset\Bbb C^{k_j}$ be a pseudoconvex domain and let $A_j\subset D_j$ be a locally pluripolar set, $j=1,...,N$. Put$$X:=\bigcup_{j=1}^N A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times...\times A_N\subset\Bbb…
This is an extended version of the talk given by the author at the NATO Advanced Study Institute "Supersymmetry and Trace Formulae" (Isaac Newton Institute, Cambridge, UK, 8-19 Septemebr 1997). Contains the following sections: 1.…
We show how geometric methods from the general theory of fractal dimensions and iterated function systems can be deployed to study symbolic dynamics in the zero entropy regime. More precisely, we establish a dimensional characterization of…
In the field of harmonic analysis, geometric considerations are frequently crucial. Specially, group actions such as translations, dilations and rotations on Euclidean space are instrumental. The objective of this paper is to extend the…
Thirty research questions on meromorphic functions and complex differential equations are listed and discussed. The main purpose of this paper is to make this collection of problems available to everyone.
This report is a combined version of two talks presented by the authors at the Edinburgh $b$-physics Workshop, December 1991. It presents the ideas of heavy quark symmetry and gives an introduction to some applications. The references…
We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a unique conjugacy class of involutions.
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
We review several recent developments in the theory and phenomenology of deep-inelastic scattering, with particular emphasis on precision tests of QCD and progress in the detailed perturbative treatment of structure functions and parton…
We give an overview of the fundamental definitions and results concerning hypersurface singularities, defined by convergent power series over an arbitrary real valued field. This approach combines, on the one hand, the classical case of…