Jack K. Hale, Hüseyin Kocak

Dynamics and Bifurcations

Illustration: Buttanri, H.

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Texts in Applied Mathematics .3
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4612-8765-0
• Softcover reprint of the original 1st ed. 1991
• Seitenzahl: 592
• Erscheinungstermin: 19. November 2011
• Englisch
• Abmessung: 235mm x 155mm x 32mm
• Gewicht: 930g
• ISBN-13: 9781461287650
• ISBN-10: 1461287650
• Artikelnr.: 36115285

Autorenporträt

The authors present the subject of dynamical systems so that it is accessible to undergraduate and beginning graduate students in mathematics or science and engineering. The fundamental ideas of dynamics and bifurcations are explained in a mathematically insightful setting, yet devoid of extensive formalism.

Inhaltsangabe

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.

Rezensionen

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