Ludwig Reich

Über einen Satz von Shl. Sternberg in der Theorie der analytischen Iterationen

AbstractLet ℂ〚X〛=ℂ〚X1,...,Xn〛 be the ring of formal power series inn indeterminates over ℂ. LetF:X→AX+B(X)=(F(1)(X),...,F(n)(X))∈(ℂ〚X〛)n denote an automorphism of ℂ〚X〛 and let ϱ1,...,ϱn be the eigenvalues of the linear partA ofF. We will say thatF has an analytic iteration (a. i.) if there exists a family (Ft(itX))t∈ℂ of automorphisms such thatFt(X) has coefficients analytic int and such thatF0=X,F1=F,Ft+t′=FtℴFt′ for allt,t′∈ℂ. Let now a setΛ=(lnϱ1,...,lnϱn) of determinations of the logarithms be given. We ask if there exists an a. i. ofF such that the eigenvalues of the linear partA(t) ofFt(X) are

Functional equation of Dhombres type – a simple equation with many open problems

e^{\ln \varrho _1 t} ,...,e^{\ln \varrho _n t}

On Covariant Embeddings of a Linear Functional Equation with Respect to an Analytic Iteration Group

. We will give necessary and sufficient conditions forF to have such an a. i., namely thatF is conjugate to a semicanonical formN=T−1ℴFℴT such that inN(k)(X) there appear at most monomialsX1α1...Xnn

Functional equation of Dhombres type in the real case

\ln \varrho _k = \sum\limits_{i = 1}^n {\alpha _i \ln } \varrho _i

Characterization of field homomorphisms by functional equations, II

. This generalizes a result of Shl.Sternberg.

Über Gruppen Von Iterativen Wurzeln Der Formalen Potenzreihe F(x) = x

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.