Invariant Manifolds, Almost Periodic and Almost Automorphic Solutions of Second-Order Monotone Equations David Cheban 1 and Cristiana Mammana 2 1 State University of Moldova Department of Mathematics and Informatics A. Mateevich Street 60 MD–2009 Chi¸ sin˘au,Moldova E-mail: cheban@usm.md 2 Institute of Economics and Finances University of Macerata str. Crescimbeni 14, I–62100 Macerata, Italy E-mail: cmamman@tin.it Abstract We give sufficient conditions of the existence of a compact invariant mani- fold, almost periodic (quasi-periodic, almost automorphic, quasi-recurrent) so- lutions and chaotic sets of the second-order differential equation x ′′ = f (t, x) on an arbitrary Hilbert space with the uniform monotone right hand side f . Keywords: non-autonomous dynamical systems; skew-product systems; cocycles; continuous invariant sections of non-autonomous dynamical systems; almost peri- odic, almost automorphic, quasi-recurrent solutions; chaotic sets 1991 Mathematics Subject Classification: primary:34C35, 34D20, 34D40, 34D45, 58F10, 58F12, 58F39; secondary: 35B35, 35B40 1 Introduction The problem of the almost periodicity of solutions of non-linear almost periodic second-order differential equations x ′′ = f (t, x) (1) 1