A Class Of Sierpinski Gaskets With Overlaps

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.