(This seminar is in-person only. No Zoom.)
The theory of semi-dynamical systems has been extended to local semi-dynamical systems and multivalued semi-dynamical systems to study the dynamics of differential equations without uniqueness, differential inclusions, and control systems. However, a theory linking these dynamical systems is still missing. In this talk, we develop a dynamical systems theory of non-global multivalued semiflows on topological spaces to capture what are brought by the combination of the locality with respect to time and the property that motions are multivalued. For this purpose, we introduce a notion of multivalued quasi-semiflows, which gives a minimal model of non-global multivalued semiflows and makes the research of this talk more than just a synthesis of local semi-dynamical systems and multivalued semi-dynamical systems. Among other things, we show that if the multivalued motion of a point $x$ clusters on a compact set, then the $\omega$-limit set of $x$ becomes nonempty. Furthermore, this non-emptiness implies the infiniteness of the maximal time of existence of the multivalued motion of $x$ under a suitable assumption of a multivalued quasi-semiflow. The results of this talk will give a foundation of the dynamical systems theory of non-global multivalued semiflows on topological spaces, which are motivated by the differential systems mentioned above.

参考文献：
J. Nishiguchi, Dynamical systems with multivalued motions: maximal time of existence and omega-limit sets, in preparation.