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- C. McMullen
- 1987

§

- C. McMullen
- 1994

We show cusps are dense in Bers' boundary for Teichm uller space. The proof rests on an estimate for the algebraic eeect of a unit quasiconformal deformation supported in the thin part of a hyperbolic Riemann surface.

- Alex Eskin, C. McMullen
- 1993

- C. McMullen, C. McMullen
- 2012

We refer to R as a general Sierpίήski carpet, after Mandelbrot [4], since Sierpiήski's universal curve is a special case of this construction [6]. It is clear that R = {J[fi(R)9 where r = \R\ and the ft are affine maps contracting R by a factor of n horizontally and m vertically. When n = m these maps are actually similarity transformations, and a well… (More)

- Peter Doyle, C. McMullen
- 1989

Equations that can be solved using iterated rational maps are characterized: an equation is ‘computable’ if and only if its Galois group is within A5 of solvable. We give explicitly a new solution to the quintic polynomial, in which the transcendental inversion of the icosahedral map (due to Hermite and Kronecker) is replaced by a purely iterative… (More)

- C. McMullen
- 1996

Any covering Y ! X of a hyperbolic Riemann surface X of-nite area determines an inclusion of Teichm uller spaces Teich(X) ,! Teich(Y). We show this map is an isometry for the Teichm uller metric if the covering is amenable, and contracting otherwise. In particular , we establish jjjj < 1 for classical Poincar e series (Kra's `Theta conjecture'). The… (More)

- C. McMullen
- 1988

Introduction.

Let X be a hyperbolic Riemann surface or orbifold, possibly of infinite topological complexity. Let φ : X → X be a quasiconformal map. We show the following conditions are equivalent (§1): (a) φ has a lift to the universal cover ∆ which is the identity on S1; (b) φ is homotopic to the identity rel the ideal boundary of X; and (c) φ is isotopic to the… (More)

- C. McMullen, J. Shearer
- IEEE Trans. Computers
- 1986

- C. McMullen
- 1988

This leads to a topological criterion for the existence of bifurcations in iterative root-finding algorithms based on rational maps (such as Newton’s method). For example, any such algorithm must fail on every neighborhood of p(X) = Xd when d is 4 or more. We show that on such neighborhoods one cannot even continuously assign to each polynomial p an… (More)