Transcendence in Algebra, Combinatorics, Geometry and Number Theory

2021

In 1994, P.-G. Becker and W. Bergweiler [8] listed all the differentially algebraic solutions of three famous functional equations: the Schröder’s, Böttcher’s and Abel’s equations. The proof of this… Expand

In the context of Riordan arrays, the problem of determining the square root of a Bell matrix $$R={\mathcal {R}}(f(t)/t,\ f(t))$$ R = R ( f ( t ) / t , f ( t ) ) defined by a formal power series… Expand

We consider formal power series f(x) = a1x+a2x + · · · (a1 6= 0), with coefficients in a field. We revisit the classical subject of iteration of formal power series, the n-fold composition f (x) =… Expand

It is shown that general solutions also exist for other values of the control parameter, not expressible in terms of known analytical functions, and a method of calculating this function numerically is proposed.Expand

A novel hybrid dynamical system comprising a continuous and a discrete state is introduced and shown to exhibit chaotic dynamics. The system includes an unstable first-order filter subject to… Expand

The aim of this paper is to study the local dynamical behaviour of a broad class of purely iterative algorithms for Newton’s maps. In particular, we describe the nature and stability of fixed points… Expand

It is shown that exact renormalization reveals a rich nonperturbative structure, and that the Jaynes-Cummings model provides a physical example of a theory with a chaotic coupling trajectory and multivalued β function.Expand