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Dynamical systems on the orbits of linear representations of Lie groups and the complete integrability of certain hydrodynamical systems

✍ Scribed by V. V. Trofimov; A. T. Fomenko

Publisher
Springer US
Year
1983
Tongue
English
Weight
585 KB
Volume
17
Category
Article
ISSN
0016-2663

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On the Spectrum, Complete Trajectories,
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✍ V.Q. Phong πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 594 KB

Let \(\{T(t)\}_{1 \geqslant 0}\) be a \(C_{0}\)-semigroup in a Banach space \(X\) with generator \(A\). We prove that if \(\{T(t)\}_{t \geqslant 0}\) is bounded and sun-reflexive, and the sun-dual semigroup is not asymptotically stable, then there exist bounded complete trajectories under \(\{T(t)\}