On rational maps with two critical points.

Milnor, John

Displaying similar documents to “On rational maps with two critical points.”

Bounded geometry of quadrilaterals and variation of multipliers for rational maps

Kevin M. Pilgrim (2004)

Fundamenta Mathematicae

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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.

Intertwined internal rays in Julia sets of rational maps

Robert L. Devaney (2009)

Fundamenta Mathematicae

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We show how the well-known concept of external rays in polynomial dynamics may be extended throughout the Julia set of certain rational maps. These new types of rays, which we call internal rays, meet the Julia set in a Cantor set of points, and each of these rays crosses infinitely many other internal rays at many points. We then use this construction to show that there are infinitely many disjoint copies of the Mandelbrot set in the parameter planes for these maps.