Ueber iterirte Functionen

  title={Ueber iterirte Functionen},
  author={Ernst Schr{\"o}der},
  journal={Mathematische Annalen},
A Survey on the Hypertranscendence of the Solutions of the Schröder’s, Böttcher’s and Abel’s Equations
  • G. Fernandes
  • Mathematics
    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
On the Square Root of a Bell Matrix
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
The generalization of Schr\"oder's theorem (1871): The multinomial theorem for formal power series under composition
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) =
A note on exact solutions of the logistic map.
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.
Exact analytic solution for a chaotic hybrid dynamical system and its electronic realization.
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
Purely Iterative Algorithms for Newton’s Maps and General Convergence
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
Renormalization Group Flow of the Jaynes-Cummings Model.
  • A. Ilderton
  • Physics, Medicine
    Physical review letters
  • 2020
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.