Аннотация:
Complex dynamical systems and nonlinear semigroup theory are not only of
intrinsic interest, but are also important in the study of evolution
problems. In recent years many developments have occurred, in particular, in
the area of nonexpansive semigroups in Banach spaces. As a rule, such
semigroups are generated by accretive operators and can be viewed as
nonlinear analogs of the classical linear contraction semigroups. Another
class of nonlinear semigroups consists of those semigroups generated by
holomorphic mappings in complex finite and infinite dimensional spaces. Such
semigroups appear in several diverse fields, including, for example, the
theory of Markov stochastic branching processes, Krein spaces and the
geometry of complex Banach spaces. In this talk based on the joint work with
M.Elin and T.Sugawa we concentrate on trends and problems related to the
nonlinear resolvent method and its connections to the classical geometric
function theory. Also some applications to complex Banach algebras will be
presented.