By providing an introduction to nonlinear differential equations, Dr Glendinning aims to equip the student with the mathematical know-how needed to appreciate stability theory and bifurcations. His approach is readable and covers material both old and new to undergraduate courses. Included are treatments of the Poincare-Bendixson theorem, the Hopf bifurcation and chaotic systems. The unique treatment that is found in this book will prove to be an essential guide to stability and chaos.
1. Introduction; 2. Stability; 3. Linear differential systems; 4. Linearization and hyperbolicity; 5. Two-dimensional dynamics; 6. Periodic orbits; 7. Perturbation theory; 8. Bifurcation theory I: stationary points; 9. Bifurcation theory II: periodic orbits and maps; 10. Bifurcational miscellany; 11. Chaos; 12. Global bifurcation theory.
'I have rarely read an introductory matematical book with such pleasure ... Those new graduate students who will use any branch of nonlinear systems theory in their studies, and who have not had the advantage of attending Dr Glendinning's final year undergraduate lectures, should sacrifice their bread and beer for the means to rush out and buy this book. More eminent and senior scientists would equally find it worth the sacrifice of a bottle or two of their favorite claret ... The book is full of excellent and appropriate examples and virtually empty of errors.' J. Brindley, Bulletin of the Institute of Mathematics 'The book has a vigorous style. Readers will also appreciate Glendinning's efforts to make it clear from the start where his discussions are going and what the important results will be ... Exercises for students, provided in each chapter, are of graded difficulty and nicely cover the material ... This book is likely to become a standard undergraduate mathematics text in non-linear differential equations.' Edward Ott, Nature 'This introduction to non-linear differential equations will prove a very useful addition to the JFM reader's library, and will play an important role in the education of future graduate students.' Journal of Fluid Mechanics 'The author writes clearly and carefully, weaving together general results with a steady supply of simple examples and excercises for the reader. Pick a section of the book to read at random and one is completely confident that effort is going to be rewarded; that the author is really explaining rather than simply recounting.' Times Higher Education Supplement