The existence of inertial functions in skew product systems

In this paper we introduce a generalization of the inertial manifold, which we call an inertial function. This is a smooth function whose graph is invariant under the dynamics, contains the global attractor, and is exponentially attracting for almost all initial conditions. The construction of this inertial function is based on the Lyapunov exponents of the dynamical system and on properties of the absorbing set.