عنوان البحث(Papers / Research Title)
The Local Connectivity Of The Mandelbrot Sets Of
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
حسنين قسام زيدان السلامي
Citation Information
حسنين,قسام,زيدان,السلامي ,The Local Connectivity Of The Mandelbrot Sets Of , Time 5/12/2011 8:20:59 AM : كلية العلوم
وصف الابستركت (Abstract)
The Local Connectivity Of The Mandelbrot Sets Of
الوصف الكامل (Full Abstract)
In this paper , we show that the Mandelbrot sets of the quadratic polynomial of the form , Where is a non-zero complex constant parameter, is locally connected at .
The local theory of iterated analytic mappings developed in the late 19 th century due to Schroder , Poincare ,Leau, Koenigs and Bottcher [10] . Douady and Hubbard proved that M ( M is Mandelbrot set ) is connected [8] . A problem is to study the local connectivity of the Julia set when ,where , is a complex parameter .Also, Douady and Hubbard gave an example of an infinitely renormalizable whose Julia set is connected but not locally connected [7] . For
an application of these general Puzzles to the study of the local connectivity of the Mandelbrot set , see [ 3] . The next important problem in this direction is to show that the Mandelbrot set is locally connected. By [9] , conjugate to ,where .
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