Systems of second-order linear ODE's with constant coefficients and their symmetries. II. The case of non-diagonal coefficient matrices

DOI10.1016/j.cnsns.2011.08.002zbMath1263.34045OpenAlexW2038348275WikidataQ58324953 ScholiaQ58324953MaRDI QIDQ430391

Otto Rutwig Campoamor Stursberg

Publication date: 21 June 2012

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2011.08.002

zbMATH Keywords

Lie algebraLevi factorpoint symmetryLie group method

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14)

Related Items

Symmetry analysis, integrability and completeness of geodesics of a double of the affine Lie group of the real line ⋮ Characterization of canonical classes for systems of linear ODEs ⋮ An alternative approach to systems of second-order ordinary differential equations with maximal symmetry. Realizations of \(\mathfrak{sl}(n+2,\mathbb{R})\) by special functions ⋮ Complete group classification of systems of two linear second-order ordinary differential equations ⋮ Generating functions and existence of contact symmetries of third order scalar ordinary differential equations ⋮ Complete group classification of systems of two nonlinear second-order ordinary differential equations of the form \(\mathbf y=\mathbf F(\mathbf y)\) ⋮ On the group classification of systems of two linear second-order ordinary differential equations with constant coefficients ⋮ Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients ⋮ Application of group analysis to classification of systems of three second-order ordinary differential equations ⋮ On certain types of point symmetries of systems of second-order ordinary differential equations ⋮ Symmetries and invariants of the systems of two linear second-order ordinary differential equations ⋮ Complete group classification of systems of two linear second‐order ordinary differential equations: the algebraic approach

Cites Work

• Unnamed Item
• Systems of second-order linear ODE's with constant coefficients and their symmetries
• Comment on ``Symmetry breaking of systems of linear second-order ordinary differential equations with constant coefficients
• Symmetry breaking of systems of linear second-order ordinary differential equations with constant coefficients
• Symmetry breaking for a system of two linear second-order ordinary differential equations
• A new geometric approach to Lie systems and physical applications
• Non-solvable contractions of semisimple Lie algebras in low dimension
• Matrix Analysis
• Symmetries of linear systems of second-order ordinary differential equations
• Lie point symmetries for systems of second order linear ordinary differential equations
• On the Lie symmetries of the classical Kepler problem