This thesis is based on Lau-Ngai's theorem,which gives a sufficient and necessary condition for an Iterated Function System of contractive similarities to verify the open set condition.Particularly,we make use of Lau-Ngai's study to investigate a class of Sierpinski gaskets with parameters??1,?2?when the images of F?1,?2 under the Iterated Function System have overlaps.The purpose of this work is to determine the conditions of the iterated function sys-tem of a class of Sierpinski gaskets with overlaps for which the open set condition is satisfied.Furthermore,we consider carefully the classification of the values??1,?2?for which the F?1,?2-Sierpinski gasket with overlaps is of?no?complete overlap. |