|Title||Global Properties of Linear Ordinary Differential Equations|
|Publisher||Kluwer Academic Publishers|
|Year of publication||1991|
|Reviewed by||VALERII V. TROFIMOV|
The linear ordinary differential equations <formula> for unknown function <formula>, are the main objects of the book under review. Differential equation for function <formula>, <formula>, is globally transformable into differential equation for function <formula>, <formula>, if there exist two functions f and h such that i) <formula> and f is non-vanishing on interval J, ii) function h is a C^n-diffeomorphism of interval J onto interval I, and the function <formula>, <formula>, is a solution whenever y is a solution. The emphasis is on the detection of the criterion of global equivalence of the ordinary differential equations. The book encloses very interesting applications of differential equations to affine differential geometry of plane curve as well,
Brief mention should be made of the contents: 1. Introduction with historical remarks; 2. Notation, definitions and some basic facts; 3. Global transformations; 4. Analytic, algebraic and geometrical aspects of global transformations; 5. Criterion of global equivalence; 6. Stationary groups; 7. Canonical forms; 8. Invariants 9. Equations with solutions of prescribed properties; 10. Zeros of solutions 11. Related results and some applications; 12. Appendix: Two functional equations.
There are additional merits of the book, concerning with search of the information. List of symbols defined in text is given. Subject index and index of names are brought.
The level is post-graduated. All consumers of the linear differential equations should find this volume very useful in theirs practical activities.
I can recommend the students, experts, and libraries alike purchase of Global Properties of Linear Ordinary Differential Equations.