从具体例子看惯性流形概念的推广

EXTENSION OF THE INERTIAL MANIFOLD CONCEPT AS SUGGESTED BY A SPECIAL CASE

惯性流形的概念要求所有轨道指数收敛于唯一吸引子[5],这对于很多物理问题,例如sine-Gordon方程是很难满足的[4],本文中给出的人工例子建议了惯性流形的推广形式,这个推广形式去掉了整体吸引子是唯一的预先要求,该推广概念使用于sine-Gordon方程。

The concept of inertial manifold[5] requires exponential convergence of all trajectories to a unique attractor, which can hardly be satisfied in many physical problems, e.g. the sine-Gordon equation[4]. Properties of an artifical example in the paper suggest a generalized form of inertial manifold, which cancels the prerequisite that the global attractor is unique. This generalized concept is used to the sine-Gordon equation.