Event № 739
Abstract: Semicocycles appear naturally in the study of the asymptotic behavior of non-autonomous differential equations. They play an important role in the theory of dynamical systems and are closely connected to semigroups of weighted composition operators. In this talk we consider semicocycles whose elements are either continuous or holomorphic mappings on a domain in a real/complex Banach space which take values in a unital Banach algebra. We study properties of semicocycles employing, in particular, their link with semigroups of nonlinear mappings. We show analogies as well as differences between the theory of semigroups and the theory of semicocycles. One of our main aims is to establish conditions for differentiability of a semicocycle and prove the existence of a "generator". The simplest semicocycles are those independent of the spatial variable. An interesting problem is to determine whether a given semicocycle is cohomologous to an independent one (in other words, is linearizable). We provide some criteria for a semicocycle to be linearizable as well as several easily verifiable sufficient conditions. This is joint work with Fiana Jacobzon and Guy Katriel.