Codesido, SantiagoFernández Tojo, Fernando Adrián2021-08-132021-08-132021Mathematics 2021, 9(8), 866; https://doi.org/10.3390/math9080866http://hdl.handle.net/10347/26806In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection. We also present a conjecture for the general case and an application to coupled harmonic oscillatorseng© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/)Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/ODEs (ordinary differential equations)ReflectionLinear systemsLiouville’s formulajournal article10.3390/math90808662227-7390open access