Uniform Methods To Establish Analytic Nomalization In The Poincaré Domain

In this thesis,a uniform scheme to handle the analytic normalization with large divisors based on the(non-)uniformly exponential dichotomy spectra of the linear parts for nonautonomous systems is shown.More precisely,the Banach space fixed with weighted norms is built at first based on the nonuniform neighborhood.Then using a uniform scheme the general stable manifold is detected,where the Poincare analytic normalization is realised.The tool utilized here is Contraction Mapping Principle in the Banach space fixed with weighted norms.In the end,the uniform theorem can be applied to autonomous systems and almost periodic systems obeying the average law to find invariant manifold with analytic normal forms on it.Comparing with others,two improvements are made.One is that the method is valid for non-autonomous systems,whose linear part admit non-uniform exponential dichotomy spectra.The other is that the norm is complicated with non-trivial weights.