Rest points of generalized dynamical systems. (English. Russian original) Zbl 0974.54026
Math. Notes 65, No. 1, 24-30 (1999); translation from Mat. Zametki 65, No. 1, 28-36 (1999).
Summary: 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.
MSC:
| 54H20 | Topological dynamics (MSC2010) |
| 26E25 | Set-valued functions |
| 54C60 | Set-valued maps in general topology |
| 58C06 | Set-valued and function-space-valued mappings on manifolds |
References:
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