Inertial invariant manifolds of a nonlinear semigroup of operators in a Hilbert space

In this paper, we examine the existence and analyze properties of inertial manifolds of a nonlinear semigroup of operators in a Hilbert space. This questions were studied in a general setting that allows generalizing results of the well-known works of K. Foias, J. Sell, and R. Temam. Our reasoning is based on the scheme of proofs of similar assertions proposed earlier by S. Sternberg and F. Hartman for ordinary autonomous differential equations.