The Rigidity Of Reducibility Of Quasi-periodic Cocycles

In this thesis,we are devoted to studying the rigidity of reducibility of quasi-periodic Cocycle,it includes two important parts:local rigidity and global rigidity.we mainly study the the rigidity of reducibility of quasi-periodic Cocycle with Dio-phantine frequency,it includes three parts:analytic,Gevrey,finite smooth.For the problem of the rigidity of reducibility,we mainly study it by KAM method.Firstly,we introduce the basic lemma,then we give the important lemma of a step of KAM and its proof.we discuss the analytic?Gevrey?finite?smooth local rigidity of reducibility of quasi-periodic Cocycle.Then we prove it by KAM iterative method.Finally,we will mainly discuss analytic?Gevrey and finite smooth global rigidity of reducibility of quasi-periodic Cocycle.Then we prove them by their local results and the renormalization scheme of Krikorian.