Example 4.12.  Example 4.10 shows that  [Graphics:Images/JuliaMandelbrotMod_gr_218.gif]  is a 2-cycle for the function  [Graphics:Images/JuliaMandelbrotMod_gr_219.gif].  It is not an attracting 2-cycle because  [Graphics:Images/JuliaMandelbrotMod_gr_220.gif]  and  [Graphics:Images/JuliaMandelbrotMod_gr_221.gif].  Hence  [Graphics:Images/JuliaMandelbrotMod_gr_222.gif],  so that  [Graphics:Images/JuliaMandelbrotMod_gr_223.gif].  

Explore Solution 4.12.

Enter the function  [Graphics:../Images/JuliaMandelbrotMod_gr_224.gif]  and point  [Graphics:../Images/JuliaMandelbrotMod_gr_225.gif]  and determine if  [Graphics:../Images/JuliaMandelbrotMod_gr_226.gif].  

[Graphics:../Images/JuliaMandelbrotMod_gr_227.gif]

[Graphics:../Images/JuliaMandelbrotMod_gr_228.gif]

Therefore,  [Graphics:../Images/JuliaMandelbrotMod_gr_229.gif]  is not an attracting 2-cycle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell