The -limit sets of quadratic Julia sets

biaccessibility in quadratic julia sets

در این رساله برای چندجمله ای های درجه ی دوم با مجموعه ی ژولیای همبند موضعی; ثابت خواهیم کرد: اندازه برولین مجموعه نقاط از دو سو دست یافتنی در چندجمله ای های درجه دو برابر با صفر است مگر چندجمله ای چبی شف که برابر با یک است. و برای چندجمله ای های درجه دوم با نقاط ثابت خنثی غیر گویا ثابت خواهیم کرد: 1)هر نقطه ی از دو سو دست یافتنی در حالت زیگل نهایتا به نقطه ی بحرانی و در حالت کرمر به نقطه ث...

Biaccessibility in Quadratic Julia Sets

This paper consists of two nearly independent parts, both of which discuss the common theme of biaccessible points in the Julia set J of a quadratic polynomial f : z 7→ z + c. In Part I, we assume that J is locally-connected. We prove that the Brolin measure of the set of biaccessible points (through the basin of attraction of infinity) in J is zero except when f(z) = z−2 is the Chebyshev map f...

Calculating Hausdorff Dimension of Julia Sets and Kleinian Limit Sets

The Solar Julia Sets of Basic Quadratic Cremer Polynomials

In general, little is known about the exact topological structure of Julia sets containing a Cremer point. In this paper we show that there exist quadratic Cremer Julia sets of positive area such that for a full Lebesgue measure set of angles the impressions are degenerate, the Julia set is connected im kleinen at the landing points of these rays, and these points are contained in no other impr...

A note on the structure of quadratic Julia sets

In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fai...