Bounded geometry of quadrilaterals and variation of multipliers for rational maps

• Autorzy: Kevin M. Pilgrim
• Języki publikacji: EN

Abstrakty

EN

Let Q be the unit square in the plane and h: Q → h(Q) a quasiconformal map. When h is conformal off a certain self-similar set, the modulus of h(Q) is bounded independent of h. We apply this observation to give explicit estimates for the variation of multipliers of repelling fixed points under a "spinning" quasiconformal deformation of a particular cubic polynomial.

Kategorie tematyczne

• 30F60: Teichm\"uller theory
• 37F10: Polynomials; rational maps; entire and meromorphic functions
• 37F30: Quasiconformal methods and Teichm\"uller theory; Fuchsian and Kleinian groups as dynamical systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 182
• Numer: 2
• Strony: 137-150

Daty

wydano

2004

Twórcy

autor

Kevin M. Pilgrim

• Department of Mathematics, Indiana University, Bloomington, IN 47401, U.S.A.

Identyfikatory

DOI

10.4064/fm182-2-4