Can semigroups be interesting? An asymptotic approach to common fixed points of semigroups of nonlinear operators acting in Banach spaces.

Abstract

This talk provides an overview of recent advancements in fixed-point theory pertaining to pointwise Lipschitzian semigroups of nonlinear operators, with a focus on the asymptotic approach. We will explore the theoretical and practical benefits of this method, highlighting its applications in both deterministic, probabilistic, and chaotic systems. Key questions will be addressed: Why focus on semigroups? Why consider nonlinearity? Why adopt a pointwise asymptotic perspective? These considerations will ultimately help us explore the intriguing potential of semigroups, as posed by the title of this lecture.