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Basic global relative invariants for homogeneous linear differential equations

About this Title

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)
MathSciNet review: 1880800
MSC (2000): Primary 34A30; Secondary 12H20, 34A25, 34M99, 35G05

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Table of Contents


  • 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

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