Progress of iteration theory since 1981

1995 ◽  
pp. 50-72
Author(s):  
György Targonski
Keyword(s):  
Iteration Theory

scholarly journals Eri Jabotinsky, mathematician and politician: a short biography

2021 ◽  
Author(s):  
Detlef Gronau
Keyword(s):  
Complete List ◽  
Iteration Theory ◽  
Short Biography ◽  
Zionist Movement

AbstractDespite the fact that Eri Jabotinsky (1910–1969) published only few (i.e. fourteen) mathematical papers, some of them had a remarkable influence in iteration theory. But also his life was remakable. Eri was the son of the famous Zionist Revisionist leader Vladimir Ze’ev Jabotinsky. Eri Jabotinsky was active in the Zionist movement and later as parlamentarian in the Knesset. Here we give an outline of his live and a complete list of his publications.

Dagger extension theorem

2011 ◽  
Vol 21 (5) ◽  
pp. 1035-1066 ◽  
Author(s):  
Z. ÉSIK ◽  
T. HAJGATÓ
Keyword(s):  
Unique Solution ◽  
Extension Theorem ◽  
Sufficient Condition ◽  
Iteration Theory ◽  
Additive Structure ◽  
Algebraic Theories ◽  
Constant Morphism

Partial iterative theories are algebraic theories such that for certain morphisms f the equation ξ = f ⋅ 〈ξ, 1p〉 has a unique solution. Iteration theories are algebraic theories satisfying a certain set of identities. We investigate some similarities between partial iterative theories and iteration theories.In our main result, we give a sufficient condition ensuring that the partially defined dagger operation of a partial iterative theory can be extended to a totally defined operation so that the resulting theory becomes an iteration theory. We show that this general extension theorem can be instantiated to prove that every Elgot iterative theory with at least one constant morphism 1 → 0 can be extended to an iteration theory. We also apply our main result to theories equipped with an additive structure.

scholarly journals Inner composition of analytic mappings on the unit disk

1991 ◽  
Vol 14 (2) ◽  
pp. 221-226 ◽  
Author(s):  
John Gill
Keyword(s):  
Fixed Point ◽  
Unit Disk ◽  
Analytic Functions ◽  
Continued Fraction ◽  
Unique Fixed Point ◽  
Iteration Theory ◽  
Basic Theorem ◽  
Closed Unit Disk ◽  
Compositional Structure ◽  
Compositional Structures

A basic theorem of iteration theory (Henrici [6]) states thatfanalytic on the interior of the closed unit diskDand continuous onDwithInt(D)f(D)carries any pointz ϵ Dto the unique fixed pointα ϵ Doff. That is to say,fn(z)→αasn→∞. In [3] and [5] the author generalized this result in the following way: LetFn(z):=f1∘…∘fn(z). Thenfn→funiformly onDimpliesFn(z)λ, a constant, for allz ϵ D. This kind of compositional structure is a generalization of a limit periodic continued fraction. This paper focuses on the convergence behavior of more general inner compositional structuresf1∘…∘fn(z)where thefj's are analytic onInt(D)and continuous onDwithInt(D)fj(D), but essentially random. Applications include analytic functions defined by this process.

scholarly journals Foundations for an iteration theory of entire quasiregular maps

2014 ◽  
Vol 201 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Walter Bergweiler ◽  
Daniel A. Nicks
Keyword(s):  
Iteration Theory

Iteration Theory: Dynamical Systems and Functional Equations

2003 ◽  
Vol 13 (07) ◽  
pp. 1627-1647 ◽  
Author(s):  
F. Balibrea ◽  
L. Reich ◽  
J. Smítal
Keyword(s):  
Dynamical Systems ◽  
Functional Equations ◽  
Discrete Dynamical Systems ◽  
Iteration Theory ◽  
Open Problems ◽  
Research Directions ◽  
The Past ◽  
New Research

The aim of this paper is to give an account of some problems considered in the past years in the setting of Discrete Dynamical Systems and Iterative Functional Equations, some new research directions and also state some open problems.

scholarly journals Conway Numbers and Iteration Theory

1997 ◽  
Vol 18 (2) ◽  
pp. 181-215 ◽  
Author(s):  
James D. Louck
Keyword(s):  
Iteration Theory
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