Résumé: Newton ’s transformation fw . z.. ¼z 1 = . wz w1 . containing only one complex parameter w ( wa or 1) is constructed from the transcendentalmapping F.... z.. ¼e z w . c : Although the number of critical points of fw . z.. is countably in .nite, a method based on the Valid Critical Point Set, vcps ¼f zkAC po . zk . pp f 0 w . zk . ¼0 ; kAZ ; is discussed for the generation of the generalized Mandelbrot set M of fw . z.. : The petalfragments, the multi- period fragments, and the classical ‘‘Mandelbrot set ’’fragments are found in M.. The dynamicalcharacteristics of fw . z.. for different values of w are analyzed. The relationship between the parameter w in a classical ‘‘Mandelbrot set ’’fragment and the structure of the corresponding .lled- in Julia set is investigated. A large number of novel images of .lled- in Julia sets are generated based on the rate of convergence of orbits.

Langue: Anglais