Linear Relations of Finite Length Modules are Shift Equivalent to Maps
Dynamical Systems
2026-05-21 v2
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. In this paper, we prove that linear relations defined on modules of finite length are shift equivalent to bijective mappings.
Keywords
Cite
@article{arxiv.2503.10829,
title = {Linear Relations of Finite Length Modules are Shift Equivalent to Maps},
author = {Bartosz Furmanek and Filip Oskar Łanecki and Mateusz Przybylski and Jim Wiseman},
journal= {arXiv preprint arXiv:2503.10829},
year = {2026}
}
Comments
Added acknowledgement, fixed references