A Liouville’s Formula for Systems with Reflection

Abstract

In 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 oscillators.

Keywords

• ODEs (ordinary differential equations)
• reflection
• linear systems
• Liouville’s formula