Space Hill Lunar Problem Of Invariant Tori And Quasi-periodic Motion

In this thesis,we mainly apply KAM theorem in the study of spatial Hill lunar prob-lem,and we will show that there exist two-dimensional invariant tori of hyperbolic type in the neighborhood of the equilibrium of this problem,moreover,we obtain two-dimensional invariant tori on the center manifold of this problem as well.This thesis is mainly divided into four parts.In chapter one,we introduce the background of three body problem and spatial Hill lunar problem,and also the related researches about this problem. In chapter two,we present some preliminaries including center manifold theorem and KAM theorem,which provide the theoretical bases for us to investigate the dynamical properties of spatial Hill lunar problem reduced on its center manifold. In chapter three,using the technique of symplectic transformation, we study the partial Birkhoff normal form of the Hamiltonian function with respect to the collinear equilibrium points. In chapter four,we show the existence of invariant tori of hyperbolic type in the neighborhood of the equilibrium points of spatial Hill lunar problem.Meanwhile by means of KAM theorem,we obtain the invariant tori for the reduced spatial Hill lunar problem on its center manifold as well.