Revisiting Sacker's work on periodic difference equations using semigroups and the Schwarzian derivative
Abstract
This article is dedicated to the memory of Robert Sacker and his contributions to the theory of difference equations. In particular, we highlight his lesser-known but mathematically rich work on semigroups of one-dimensional mappings characterized by a nonnegative modified Schwarzian derivative. These semigroups provide verifiable analytic conditions for establishing global stability in periodic difference equations. Using some recent work on the Schwarzian derivative of rational functions, we extend Sacker's results to rational functions whose zeroes and poles are simple and interlaced.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Differential Equations and Dynamical Systems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- The Journal of Difference Equations and Applications
- Volume
- 32
- Issue
- 5
- Pages
- 764–771
- Publication date
- 27 February 2026
- Language
- EN