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

The concept of inertial manifold5 requires exponential convergence of all trajectories to a unique attractor, which can hardly be satisfied in many physical problems, e.g. the sine-Gordon equation4. 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.