5 papers
On quasiregular linearizers
Alastair Fletcher, Douglas Macclure
Linearization is a well-known concept in complex dynamics. If is a polynomial and is a repelling fixed point, then there is an entire function which conjugates to…
Dynamics of mappings with constant dilatation
Alastair Fletcher, Robert Fryer
Let h:C \to C be an R-linear map. In this article, we explore the dynamics of the quasiregular mapping H(z)=h(z)^2. Via the Böttcher type coordinate constructed in "On Böttcher coo…
On Böttcher coordinates and quasiregular maps
Alastair Fletcher, Robert Fryer
It is well-known that a polynomial f(z)=a_d z^d(1+o(1)) can be conjugated by a holomorphic map phi to w \mapsto w^d in a neighbourhood of infinity. This map phi is called a Böttche…
The Moduli space of Riemann Surfaces of Large Genus
Alastair Fletcher, Jeremy Kahn, Vladimir Markovic
Let be the -thick part of the moduli space of closed genus surfaces. In this article, we show that the number of balls of radius need…
Quasiregular mappings of polynomial type in R^2
Alastair Fletcher, Dan Goodman
Complex dynamics deals with the iteration of holomorphic functions. As is well- known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials,…