一类超线性可逆系统的Aubry-Mather集

Aubry-Mather Sets for a Class of Superlinear Reversible Systems

通过引进合适的作用—角变量变换,运用新的估计方法,对超线性可逆系统的Pomcare映射应用推广的平面可逆系统的Aubry-Mather定理,在系统光滑性为C^1的情形下,证明了一类超线性可逆系统的Aubry-Mather集的存在性.

By introducing an appropriate action-angle variable transformation and using a new estimate method, the author obtains the existence of Aubry-Mather sets to a class of superlinear reversible systems whose smoothness is C^1, via Aubry-Mather theorem of generalized planar reversible systems on Poincare map of reversible systems.