Basic global relative invariants for nonlinear differential equations / Roger Chalkley.

Format:

Book

Author/Creator:

Chalkley, Roger, 1931- author.

Series:

Memoirs of the American Mathematical Society ; Volume 190, Number 888.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 190, Number 888

Language:

English

Subjects (All):

Differential equations, Nonlinear.

Invariants.

Physical Description:

1 online resource (386 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2007.

Language Note:

English

Summary:

The problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order $m$ was initiated in 1879 with Edmund Laguerre's 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 equa

Contents:

""Part 3. Supplementary Results""

Notes:

"Volume 190, Number 888 (first of three numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0494-X