Abstract
In this paper we consider generalized dynamical systems whose integral vortex (that is, the set of all trajectories of the system starting at a given point) is an acyclic set in the corresponding space of curves. For such systems we apply the theory of fixed points for multi-valued maps in order to prove the existence of rest points. In this way we obtain new existence theorems for rest points of generalized dynamical systems.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 28–36, January, 1999.
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Gel’man, B.D. Rest points of generalized dynamical systems. Math Notes 65, 24–30 (1999). https://doi.org/10.1007/BF02675006
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DOI: https://doi.org/10.1007/BF02675006