5 citations · 11 across the 15 of their papers we have counts for
19 papers
Forward limit sets of semigroups of substitutions
Ibai Aedo, Uwe Grimm, Ian Short
We introduce the forward limit set of a semigroup generated by a family of substitutions of a finite alphabet, which typically coincides with the set of all possible s-adic…
Necessary and sufficient conditions for convergence of integer continued fractions
Ian Short, Margaret Stanier
Fundamental to the theory of continued fractions is the fact that every infinite continued fraction with positive integer coefficients converges; however, it is unknown precisely w…
Nilpotent covers of symmetric and alternating groups
Nick Gill, Ngwava Arphaxad Kimeu, Ian Short
We prove that the symmetric group has a unique minimal cover by maximal nilpotent subgroups, and we obtain an explicit and easily computed formula for the order…
Stability of the Denjoy-Wolff Theorem
Argyrios Christodoulou, Ian Short
The Denjoy-Wolff theorem is a foundational result in complex dynamics, which describes the dynamical behaviour of the sequence of iterates of a holomorphic self-map of the unit…
A hyperbolic-distance inequality for holomorphic maps
Argyrios Christodoulou, Ian Short
We prove an inequality which quantifies the idea that a holomorphic self-map of the disc that perturbs two points is close to the identity function.
Repeated compositions of Moebius transformations
Matthew Jacques, Ian Short
This paper considers a class of dynamical systems generated by finite sets of Moebius transformations acting on the unit disc. Compositions of such Moebius transformations give ris…