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Infinite Iterated Function Systems Depending on a Parameter

Ludwik Jaksztas (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

This paper is motivated by the problem of dependence of the Hausdorff dimension of the Julia-Lavaurs sets J 0 , σ for the map f₀(z) = z²+1/4 on the parameter σ. Using homographies, we imitate the construction of the iterated function system (IFS) whose limit set is a subset of J 0 , σ , given by Urbański and Zinsmeister. The closure of the limit set of our IFS ϕ σ , α n , k is the closure of some family of circles, and if the parameter σ varies, then the behavior of the limit set is similar to the behavior of J 0 , σ . The parameter...

Intertwined internal rays in Julia sets of rational maps

Robert L. Devaney (2009)

Fundamenta Mathematicae

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.

Intertwined mappings

Jean Ecalle, Bruno Vallet (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Introduction

Pascale Roesch (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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