Abstract: In this paper, the generalized Kuramoto-Sivashinsky equations (GKS)withperiodic initial boundary value problem are considered and the construction of inertialsets in space H₂ is given. Furthermore this paper gives and find out an exponentially approximating of attractors for GKS equations and find out an exponentially approximatingsequence of compact fractal localizing sets of the attractors, these results sharpen and improve the conclusions of the conclusions of the inertial sets and attractor.for GKS equation in [l, 3, 5,7]. which describe a kind of geometrical structure of the attractors.

Key words: GKS equation, attractor, inertial set, fractal structure