Reducibility Of Quasi-periodic Schr(?)dinger-Cocycle

In this thesis,we study both local and global reducibility problems concerning quasi-periodic Schr(?)dinger-Cocycle.When the analytic quasi-periodic Schr(?)dinger-Cocycle is close to constant Cocycle,we discuss the local reducibility property of quasi-periodic Schr(?)dinger-Cocycle for energies of a set of full measure and the local rotations reducibility property for energies of a set of positive measure.When this Cocycle is not close to constant Cocycle,we discuss the global reducibility property of this Cocycle for energies of a set of full measure.The content of this thesis is organized as follows:·In the first chapter,we introduces some backgrounds of reducibility problem-s concerning quasi-periodic Cocycle and the main problems discussed in the paper.·In the preliminary knowledge of chapter 2,the first section introduces norms and function spaces involved in this paper.In the second section,we introduce the knowledge of quasi-periodic linear Cocycle.The third section introduces an important lemma,which is very important to prove the main theorem.The fourth section gives the concept of Z2-action,which we will use when we use renormalizations.The fifth section introduces some conditions of number theory.·In chapter 3,we combine the fundamental lemma to demonstrate the local reducibility property of quasi-periodic Schr(?)dinger-Cocycle for energies of a set of full measure for Diophantine frequencies when the fiber rotations number satisfies some number theory conditions.·In chapter 4,we apply the improved iterative method to deal with the proof of local rotations reducibility for energies of a set of positive measure for quasi-periodic Schr(?)dinger-Cocycle under one-dimensional Liouvillean frequencies.·On the basis of local reducibility in chapter 5,we use the method of renormal-izations to consider global reducibility problems of quasi-periodic Schr(?)dinger-Cocycle in one-dimensional case.