Dynamics and Bifurcations
(Sprache: Englisch)
This book of ideas and examples about the geometry of dynamics and bifurcations of ordinary differential equations. The subject of differential and difference equations is an old and much-honored chapter in science. In recent years, due primarily to the...
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Klappentext zu „Dynamics and Bifurcations “
This book of ideas and examples about the geometry of dynamics and bifurcations of ordinary differential equations. The subject of differential and difference equations is an old and much-honored chapter in science. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications. It is the aim of this book to provide a modest foundation of knowledge for undergraduate and beginning graduate students in mathematics or science and engineering. Equations in dimension one and two constitute the majority of the text. It is demonstrated in particular that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations. Proceeding, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits, appear.
Inhaltsverzeichnis zu „Dynamics and Bifurcations “
Part I: Dimension OneChapter 1. Scalar Autonomous Equations
Chapter 2. Elementary Bifurcations
Chapter 3. Scalar Maps
Part II: Dimension One and One Half
Chapter 4. Scalar Nonautonomous Equations
Chapter 5. Bifurcation of Periodic Equations
Chapter 6. On Tori and Circles
Part III: Dimension Two
Chapter 7. Planar Autonomous Systems
Chapter 8. Linear Systems
Chapter 9. Near Equilibria
Chapter 10. In the Presence of a Zero Eigenvalue
Chapter 11. In the Presence of Purely Imaginary Eigenvalues
Chapter 12. Periodic Orbits
Chapter 13. All Planar Things Considered
Chapter 14. Conservative and Gradient Systems
Chapter 15. Planar Maps
Part IV: Higher Dimensions
Chapter 16. Dimension Two and One Half
Chapter 17. Dimension Three
Chapter 18: Dimension Four
Farewell
Appendix: A Catalogue of Fundamental Theorems
References
Index
Bibliographische Angaben
- Autoren: Jack K. Hale , Hüseyin Kocak
- 2006, 574 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Illustration:Buttanri, H.
- Verlag: Springer, New York
- ISBN-10: 0387971416
- ISBN-13: 9780387971414
- Erscheinungsdatum: 15.11.1996
Sprache:
Englisch
Rezension zu „Dynamics and Bifurcations “
J.K. Hale, H. Kocak, and H. Buttanri
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