Chain Reversal System Solution Of Nekhoroshev Stable

In this paper, by the use of Nekhoroshev technology, we proved solutions on the initial value for a long time stability of an infinite dimensional reversible system.In Chapter 1, we introduces the Nekhoroshev estimate the background, significance and status of domestic and foreign research and this paper's main work.In Chapter 2, we describe the exponential stability of 1-dimension torus. Further, in the case of short range interaction among the particle, one has that the above periodic orbit is exponentially localized in space.In Chapter 3, by the promotion of content of previous chapter, we describe the exponential stability of n-dimension torus.In Chapter 4, we prove Normal Form Theorem of the general reverse system.In Chapter 5, we prove the theorem of the exponential stability on periodic and quasi-periodic breathers.