Ulteriori informazioni
The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps a more mature look. Many of the available books and expository narratives either require extensive mathematical preparation, or are not designed to be used as textbooks. The authors have filled this void with the present book.
Sommario
I: Dimension One.- 1. Scalar Autonomous Equations.- 2. Elementary Bifurcations.- 3. Scalar Maps.- II: Dimension One and One Half.- 4. Scalar Nonautonomous Equations.- 5. Bifurcation of Periodic Equations.- 6. On Tori and Circles.- III: Dimension Two.- 7. Planar Autonomous Systems.- 8. Linear Systems.- 9. Near Equilibria.- 10. In the Presence of a Zero Eigenvalue.- 11. In the Presence of Purely Imaginary Eigenvalues.- 12. Periodic Orbits.- 13. All Planar Things Considered.- 14- Conservative and Gradient Systems.- 15. Planar Maps.- IV: Higher Dimensions.- 16. Dimension Two and One Half.- 17. Dimension Three.- 18. Dimension Four.- Farewell.- APPENDIX: A Catalogue of Fundamental Theorems.- References.
Riassunto
Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations.
Relazione
J.K. Hale, H. Kocak, and H. Buttanri
Dynamics and Bifurcations
"This book takes the reader step by step through the vast subject of dynamical systems. Proceeding from 1 to 2 dimensions and onto higher dimensions in separate self-contained sections, the text is mathematically rigorous yet devoid of excess formalism. A refreshing balance is further achieved by the use of many excellent illustrations and a wealth of worked and unworked examples."-MATHEMATIKA
