Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Bounded geometry of quadrilaterals and variation of multipliers for rational maps

100%

Pilgrim K.

Fundamenta Mathematicae

2004

tom 182

nr 2

137-150

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.

Dynamic classification of escape time Sierpiński curve Julia sets

63%

Devaney R., Pilgrim K.

Fundamenta Mathematicae

2009

tom 202

nr 2

181-198

For n ≥ 2, the family of rational maps $F_{λ}(z) = zⁿ + λ/zⁿ$ contains a countably infinite set of parameter values for which all critical orbits eventually land after some number κ of iterations on the point at infinity. The Julia sets of such maps are Sierpiński curves if κ ≥ 3. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Möbius or anti-Möbius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of n and κ.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Pilgrim K.

1 Devaney R.

1 2009

1 2004

Wyniki wyszukiwania

Bounded geometry of quadrilaterals and variation of multipliers for rational maps

Dynamic classification of escape time Sierpiński curve Julia sets