# Basic Global Relative Invariants for Nonlinear Differential Equations Roger Chalkley

#### 365 pages

Description Basic Global Relative Invariants for Nonlinear Differential Equations by Roger Chalkley
October 28th 2007 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 365 pages | ISBN: 9780821839911 | 7.33 Mb

The problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order \$m\$ was initiated in 1879 with Edmund Laguerres success for the special case \$m = 3\$.

It was solved in number 744 of theMoreThe problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order \$m\$ was initiated in 1879 with Edmund Laguerres success for the special case \$m = 3\$. It was solved in number 744 of the Memoirs of the AMS (March 2002), by a procedure that explicitly constructs, for any \$m /geq3\$, each of the \$m - 2\$ basic relative invariants. During that 123-year time span, only a few results were published about the basic relative invariants for other classes of ordinary differential equations.

With respect to any fixed integer \$/,m /geq 1\$, the author begins by explicitly specifying the basic relative invariants for the class \$/,/mathcal{C {m,2 \$ that contains equations like \$Q {m = 0\$ in which \$Q {m \$ is a quadratic form in \$y(z), /, /dots, /, y{(m) (z)\$ having meromorphic coefficients written symmetrically and the coefficient of \$/bigl( y{(m) (z) /bigr){2 \$ is \$1\$.Then, in terms of any fixed positive integers \$m\$ and \$n\$, the author explicitly specifies the basic relative invariants for the class \$/,/mathcal{C {m,n \$ that contains equations like \$H {m,n = 0\$ in which \$H {m,n \$ is an \$n\$th-degree form in \$y(z), /, /dots, /, y{(m) (z)\$ having meromorphic coefficients written symmetrically and the coefficient of \$/bigl( y{(m) (z) /bigr){n \$ is \$1\$.

These results enable the author to obtain the basic relative invariants for additional classes of ordinary differential equations.

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