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On a problem of J. Hale. (Russian) Zbl 0714.34073
To a problem formulated by J. K. Hale [Lect. Notes Math. 799, 152- 172 (1980; Zbl 0433.34056)] a partial answer is given by the following theorem: Let the cascade (X,P) be pointwise dissipative and locally bounded, and let the mapping P be $$\alpha$$-condensing; then (X,P) admits a maximal compact invariant manifold K.
Reviewer: W.Müller
##### MSC:
 37-XX Dynamical systems and ergodic theory 34C30 Manifolds of solutions of ODE (MSC2000)