The Lagrange Stability Of An Isochronous System With A Singularity Under Unbounded Perturbation

It has been 50 years since Littlewood problem was proposed at 1960's. During the past years, many authors in China or aboard have taken attention to this problem and made a comprehensive study. Moser's twist theorems are powerful tools to deal with this problem. After summarizing the main developments of this problem briefly, we investigate the complicated dynamical behaviors of an isochronous system with a repulsive singularity under time-dependent and unbounded perturbation, Lagrangc stability and the existence of qusi-periodic solution.This thesis is divided into three chapters. In the first one, we make a description of Littlewood problem and give a brief summary of important de-velopments of this problem. At the same time, we also indicate the general idea of handling this problem. Then, we set out the basic definitions and prop-erties of Hamilton system in chapter two, which is necessary for the research of Hamilton system. Certainly, Moser's twist theorems arc also one part of the preliminary. But we just simply list the conclusions of Moser's twist theorem and its variant. In the last chapter, we give out our conclusion and a brief proof.