Template Iterations of Quadratic Maps and Hybrid Mandelbrot Sets

Quasi-Mandelbrot sets for perturbed complex analytic maps: visual patterns

We consider perturbations of the complex quadratic map $ z \to z^2 +c$ and corresponding changes in their quasi-Mandelbrot sets. Depending on particular perturbation, visual forms of quasi-Mandelbrot set changes either sharply (when the perturbation reaches some critical value) or continuously. In the latter case we have a smooth transition from the classical form of the set to some forms, cons...

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...

Template iterations and maximal cofinitary groups

In [2], Jörg Brendle used Hechler’s forcing notion for adding a maximal almost family along an appropriate template forcing construction to show that a (the minimal size of a maximal almost disjoint family) can be of countable cofinality. The main result of the present paper is that ag, the minimal size of maximal cofinitary group, can be of countable cofinality. To prove this we define a natur...

Semi-θ-Open Sets and New Classes of Maps

FRACTAL n-GONS AND THEIR MANDELBROT SETS

We consider self-similar sets in the plane for which a cyclic group acts transitively on the pieces. Examples like n-gon Sierpiński gaskets, Gosper snowflake and terdragon are well-known, but we study the whole family. For each n our family is parametrized by the points in the unit disk. Due to a connectedness criterion, there are corresponding Mandelbrot sets which are used to find various new...