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Motions of semicontinuous semidynamical systems in the plane which are stable in Poisson’s sense. (Russian) Zbl 0599.34064
An important theorem in the Poincaré-Bendixson theory of dynamical systems is the theorem on the existence of a fundamental point inside a domain bounded by a closed trajectory. Continuing earlier investigations of A. D. Myshkis on the stationary point of a dynamical system inside a closed trajectory [Mat. Sb., Nov. Ser. 34(76), 525-540 (1954; Zbl 0056.083)] here the theorem mentioned above is transferred to the case of semicontinuous semidynamical systems. Furthermore some theorems on motions of semicontinuous semidynamical systems in the plane stable in Poisson’s sense are proved.
Reviewer: K.Barckow
MSC:
37-XX Dynamical systems and ergodic theory
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