THE RATIONAL - SYSTEM WITH THE LIMIT SET CONSISTING CONNECTIVITY COMPONENTS - Ruzimuradova Durdona Xamidjonovna (Web of Journals Publishing, 2024)
Studying the structure of a limit set is crucial for characterizing the long-term behavior and stability of a dynamical system. It is known that a bounded limit set is a continuum i.e. connected and compact, whereas unbounded ones may have enough complicated structure [1- 11]. For instance, the limit set of -system may consist of uncountable connectivity components. It can be shown that -limit set of quadratic systems is always connected. There is a cubic system on the plane which possesses the -limit set consisting of two straight lines. The limit set of a polynomial system on the plane may have connectivity components for arbitrary large [2]. In this paper we consider a problem how to construct a rational dynamical system with the -limit set consisting connectivity components.
Keywords: dynamical system, rational system, vector field, limit set, Hamiltonian system, Hamiltonian function, connectivity components, unboundedness.