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# memo_has_moved_text();Basic global relative invariants for homogeneous linear differential equations

Roger Chalkley

Publication: Memoirs of the American Mathematical Society
Publication Year 2002: Volume 156, Number 744
ISBNs: 978-0-8218-2781-9 (print); 978-1-4704-0337-9 (online)
DOI: http://dx.doi.org/10.1090/memo/0744
MathSciNet review: 1880800
MSC: Primary 34A30; Secondary 12H20, 34A25, 34M99, 35G05

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Chapters

• 1. Introduction
• 2. Some problems of historical importance
• 3. Illustrations for some results in Chapters 1 and 2
• 4. $L_n$ and $I_{n,i}$ as semi-invariants of the first kind
• 5. $V_n$ and $J_{n,i}$ as semi-invariants of the second kind
• 6. The coefficients of transformed equations
• 7. Formulas that involve $L_n(z)$ or $I_{n,n}(z)$
• 8. Formulas that involve $V_n(z)$ or $J_{n,n}(z)$
• 9. Verification of $I_{n,n} \equiv J_{n,n}$ and various observations
• 10. The local constructions of earlier research
• 11. Relations for $G_i$, $H_i$, and $L_i$ that yield equivalent formulas for basic relative invariants
• 12. Real-valued functions of a real variable
• 13. A constructive method for imposing conditions on Laguerre-Forsyth canonical forms
• 14. Additional formulas for $K_{i,j}$, $U_{i,j}$, $A_{i,j}$, $D_{i,j}$, …
• 15. Three canonical forms are now available
• 16. Interesting problems that require further study