عنوان البحث(Papers / Research Title)
Some Geometric Properties of Julia Sets of Maps
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
افتخار مضر طالب الشرع
Citation Information
افتخار,مضر,طالب,الشرع ,Some Geometric Properties of Julia Sets of Maps , Time 5/15/2011 7:16:36 AM : كلية التربية للعلوم الصرفة
وصف الابستركت (Abstract)
In this work, we will study the geometric properties of Julia sets of the quadratic polynomial maps
الوصف الكامل (Full Abstract)
Some Geometric Properties of Julia Sets of Maps
In this work, we will study the geometric properties of Julia sets of the quadratic polynomial maps of the form where is a non-zero complex .
We show that Julia set is the unit circle if c =2 and Julia set is the line segment if c=4 . If 1<z<2.3 .
Then the Julia set is a simple closed curve ,also if 1<z<2.3 then the Julia set is a simple closed curve such that Julia set which contains no smooth arcs, and if then the Julia set is infinitely many different simple closed curves.
In complex dynamics , the iteration theory originated in 1910 [7] . Among the most important concepts in complex dynamics are Julia sets .They were studied by the French mathematician Gaston Julia (1893 – 1978 ) ,
who developed much of theory when he was recovering from his wounds in an army hospital during world war I . He published a long paper in French language in [4],
Julia and Fatou looked at the iteration of the simplest quadratic map of the form ( ) .
In general ,distinct maps have distinct Julia sets , however , there exist distinct polynomial maps , rational maps and entire maps that have the same Julia sets [5], [6].The Julia set of a polynomial typically has a complicated , self – similar structure. Therefore the Julia sets are fractals [2] ,[7] .
However , there exist rational maps whose Julia sets fail to be quasi-self-similar [3] .
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