The necessary conditions of the preservation of an invariant manifold of an autonomous system near an equilibrium point |
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Authors: | George Osipenko Eugene Ershov |
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Institution: | (1) Dept of Mathematics, State Technical University, St. Petersburg;(2) Dept of Mathematics, Civil Engineering Institute, St. Petersburg, Russia |
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Abstract: | Let a smooth autonomous system of ordinary differential equations have a smooth locally invariant manifold passing through its equilibrium point. The sufficient conditions are known under which each perturbed system has at least one smooth invariant manifoldC
1 close to the original one. In the paper we prove the necessity of these conditions. |
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