The k-compound of a difference-algebraic system

The multiplicative and additive compounds of a matrix have important applications in geometry, linear algebra, and the analysis of dynamical systems. In particular, the k-compounds allow to build a k-compound dynamical system that tracks the evolution of k-dimensional parallelotopes along the original dynamics. This has recently found many applications in the analysis of non-linear systems described by ODEs and difference equations. Here, we introduce the k-compound system corresponding to a difference-algebraic system, and describe several applications to the analysis of discrete-time dynamical systems.(c) 2023 Elsevier Ltd. All rights reserved.