Linear Relations of Finite Length Modules are Shift Equivalent to Maps
Abstract
Abstract Linear relations, defined as submodules of the direct sum of two modules, can be viewed as objects that carry dynamical information and reflect the inherent uncertainty of sampled dynamics. These objects also provide an algebraic structure that enables the definition of subtle invariants for dynamical systems. By recognizing specific categorical aspects of these objects, we prove that linear relations defined on modules of finite length are shift equivalent to bijective mappings.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Polynomial and algebraic computation
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Qualitative Theory of Dynamical Systems
- Publisher
- Springer Science and Business Media LLC
- Volume
- 25
- Issue
- 3
- Publication date
- 20 May 2026
- Language
- EN