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memo_has_moved_text();Basic global relative invariants for nonlinear differential equations

Roger Chalkley

Publication: Memoirs of the American Mathematical Society
Publication Year 2007: Volume 190, Number 888
ISBNs: 978-0-8218-3991-1 (print); 978-1-4704-0494-9 (online)
DOI: http://dx.doi.org/10.1090/memo/0888
MathSciNet review: 2356350
MSC: Primary 34A34; Secondary 12H20, 34A25, 34C14, 34M15

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Chapters

• Part 1. Foundations for a general theory
• 1. Introduction
• 2. The coefficients $c^*_{i,j}(z)$ of (1.3)
• 3. The coefficients $c^{**}_{i,j}(\zeta )$ of (1.5)
• 4. Isolated results needed for completeness
• 5. Composite transformations and reductions
• 6. Related Laguerre-Forsyth canonical forms
• Part 2. The basic relative invariants for $Q_m=0$ when $m\ge 2$
• 7. Formulas that involve $L_{i,j}(z)$
• 8. Basic semi-invariants of the first kind for $m \geq 2$
• 9. Formulas that involve $V_{i,j}(z)$
• 10. Basic semi-invariants of the second kind for $m \geq 2$
• 11. The existence of basic relative invariants
• 12. The uniqueness of basic relative invariants
• 13. Real-valued functions of a real variable
• Part 3. Supplementary results
• 14. Relative invariants via basic ones for $m \geq 2$
• 15. Results about $Q_m$ as a quadratic form
• 16. Machine computations
• 17. The simplest of the Fano-type problems for (1.1)
• 18. Paul Appell’s condition of solvability for $Q_m = 0$
• 19. Appell’s condition for $Q_2 = 0$ and related topics
• 20. Rational semi-invariants and relative invariants
• Part 4. Generalizations for $H_{m,n}=0$
• 21. Introduction to the equations $H_{m,n} = 0$
• 22. Basic relative invariants for $H_{1,n} = 0$ when $n \geq 2$
• 23. Laguerre-Forsyth forms for $H_{m,n} = 0$ when $m \geq 2$
• 24. Formulas for basic relative invariants when $m \geq 2$
• 25. Extensions of Chapter 7 to $H_{m,n} = 0$, when $m \geq 2$
• 26. Extensions of Chapter 9 to $H_{m,n} = 0$, when $m \geq 2$
• 27. Basic relative invariants for $H_{m,n} = 0$ when $m \geq 2$
• Part 5. Additional classes of equations
• 28. The class of equations specified by $y”(z) y’(z)$
• 29. Formulations of greater generality
• 30. Invariants for simple equations unlike (29.1)