Finite IP-Independent Set And Its Related Problems In Dynamical System

We discuss the properties of finite IP-independent sets and related problems in the countable compact space in this passage.In the first chapter,some basic knowledges concerning the background and status of dynamical system and ergodic theory are given.In the second chapter,we prove the theorem that for any system,if the degree of its derived set is less than or equal to 1,then it's null,so there doesn't exist any finite IP-independent pairs in this system.And then an example of topology dynamical system is given to show that finite IP-independent pairs are different from topology sequence pairs.In the last chapter,by proving the existence of finite IP-independent sets,we prove that when the derived degree of space X is greater than 1,there exists a system(X,T),any pair consists of elements in Xd can be a finite IP-independent pair.