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Some Topological properties of Julia sets of maps
In this work, we study the topological properties of Julia sets of the quadratic polynomial maps .
Complex dynamics is the study of iteration of maps which map the complex plane into itself . In general , their dynamics are quite complicated and hard to explain ,their dynamics are quite complicated and hard to explain ,but for some classes of maps , many interesting results can be proved .
For example , one often studies the Julia sets of polynomial maps .
The Julia set of the quadratic map of the form was studied extensively .
From a dynamical systems point of view , all of the interesting behavior of a complex analytic map occurs on its Julia set , it is this set that contains the interesting topology .
The idea behind the Julia sets is to study whether the absolute value of a point in the complex plane converges towards infinity or not ,
when it is iterated under a map . All the points that do not go toward infinity ,
when iterated , are in the Julia set .
- وصف الــ Tags لهذا الموضوع
- Julia sets, quadratic polynomial
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