The Nature Of The Periodic Function Of The Hamiltonian System With A Critical Point

Nonlinear dynamics, more grandly called "nonlinear science"or"chaos theory", is an impor-tant subject, which plays an important role in the study of almost all disciplines of science. Includ-ing mathematics, mechanical, aerospace, electrical, control systems, population problems and so on. In general, dynamics systems will be included in certain parameters (usually called bifurcation parameters or control parameters). Changes in these parameters of the study of the behavior of dynamical systems has played a significant role in. The complex dynamics phenomena, including instability, bifurcation and chaos. Nonlinear dynamic systems can be roughly divided into two aspects:local analysis and global analysis. Both types should use different methods and theories to study.One branch of theory is dependent on the parameters for the system we studied the pa-rameters of a particular value of the vicinity small changes, fundamental changes in the nature of the situation.Branch in the theory of differential equations,mainly in a critical value of parameter changes near the critical point when the number of changes, changes in the stability of singular points, periodic changes in the number of issues.Branch is common in nature Them, and thus large numbers in the description of the mathematical models of natural phenomena.This paper studies periodic function of the global nature of the Hamiltonian system, including monotonicity and convex-concave. Research method mainly used in computer numerical calcula-tion and symbolic operation. For example, a study using a computer draw system, trajectory map, to a large number of complex mathematical calculations. The contents of this paper is as follows:As an introduction, in the first chapter we introduce the background of our research and main topics that we will study in the following chapters. We also give a description of our methods and results detained in this thesis in the first chapter.The second chapter describes the symbols associated with the paper said, and some knowl-edge of the preparatory theorems.Chapter III studies a form of Hamiltonian systems with a periodic function, and proved that such a periodic function is a monotone increasing and is a convex function.Finally, in chapter IV, the first proof of another form of Hamiltonian systems to determine the nature of periodic function and we give the proof of Theorem. Periodic function to be proved of another form, and proved that such a periodic function is a monotone increasing and is a convex function.