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Sufficient conditions for the conservation of an invariant manifold at vertical perturbations. (Russian) Zbl 0599.34061

In Differ. Uravn. Dinam. Sistemy-Kishinev, 25-31 (1985) the author studied problems on the decomposition of weakly nonlinear extensions of dynamical systems.
Continuing those former investigations and using results of Grobman and Hartman on the extensions of dynamical systems the theorem of M. W. Hirsch, C. C. Pugh and M. Shub on the conservation of a smooth invariant manifold is generalized for the case of extensions of dynamical systems.
Reviewer: K.Barckow

MSC:

37-XX Dynamical systems and ergodic theory
34C40 Ordinary differential equations and systems on manifolds
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