**(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.