Characterization of the class of canonical forms for systems of linear equations

2015/02/25 by J. C. Ndogmo, Ndogmo, JC
Computer Science · Mathematics · Physics and Astronomy · #34A30 #58D19 #65F10 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1502.07164

openalex publication_date 2015/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical equation \by⁽ⁿ⁾=0 consists of copies of the same iterative equation. Other properties of iterative linear systems are also derived, as well as the superposition formula for their general solution.

Citations

• On point transformations of linear equations of maximal symmetry

Related

• Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis
• Belitskii's canonical forms of linear dynamical systems
• On point transformations of linear equations of maximal symmetry
• A note on the transformation of the linear differential equation into a system of the first order equations
• Formulae of Partial Reduction for Linear Systems of First Order Operator Equations