TY  - BOOK
AU  - Chalkley,Roger
TI  - Basic global relative invariants for nonlinear differential equations
T2  - Memoirs of the American Mathematical Society, 
SN  - 9781470404949 (online)
AV  - QA371 .C435 2007
U1  - 515/.355 22
PY  - 2007///
CY  - Providence, R.I.
PB  - American Mathematical Society
KW  - Differential equations, Nonlinear
KW  - Invariants
N1  - "November 2007, volume 190, number 888 (first of three numbers)."; Includes bibliographical references (p. 357-358) and index; 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); Access is restricted to licensed institutions; Electronic reproduction; Providence, Rhode Island; American Mathematical Society; 2012
UR  - http://www.ams.org/memo/0888
UR  - http://dx.doi.org/10.1090/memo/0888
ER  -