Koksch, Norbert A modified strong squeezing property and the existence of inertial manifolds of semiflows. (English) Zbl 1072.37053 Arch. Math., Brno 36, Suppl., 477-486 (2000). Sometimes so-called cone invariance and squeezing properties are used to show the existence of inertial manifolds for evolution equations. The author propose and motivate a modification of these properties for semiflows. It is shown that the cone invariance and modified squeezing properties together with a coercivity assumption are sufficient for a general, continuous semiflow to have an inertial manifold with exponential tracking property. An application to evolution equations is considered and some possible extensions are discussed as well. Reviewer: Josef DiblĂk (Brno) MSC: 37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 37D10 Invariant manifold theory for dynamical systems 34C30 Manifolds of solutions of ODE (MSC2000) Keywords:semiflow; inertial manifold; asymptotic phase; cone invariance property PDF BibTeX XML Cite \textit{N. Koksch}, Arch. Math., Brno 36, 477--486 (2000; Zbl 1072.37053) Full Text: EuDML EMIS OpenURL