Dynamics and Bifurcations

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...

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Bibliographic Details
Main Authors Hale, Jack K, Buttanri, H, Kocak, Hüseyin
Format eBook
LanguageEnglish
Published New York, NY Springer New York 1991
Edition1
SeriesTexts in Applied Mathematics
Subjects
Analysis
Complex Systems
Differential equations
Global analysis (Mathematics)
Mathematics
Mathematics and Statistics
Statistical physics
Statistical Physics and Dynamical Systems
Online AccessGet full text
ISBN1461287650
9781461287650
9780387971414
9781461244271
0387971416
1461244277
ISSN0939-2475
DOI10.1007/978-1-4612-4426-4

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Table of Contents:
  • Intro -- Texts in Applied Mathematics -- Dynamics and Bifurcations -- Copyright -- Greeting -- Contents -- 1 D -- 1 Scalar Autonomous Equations -- 2 Elementary Bifurcations -- 3 Scalar Maps -- 1½ D -- 4 Scalar Nonautonomous Equations -- 5 Bifurcations of Periodic Equations -- 6 On Tori and Circles -- 2 D -- 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 -- 2½+ D -- 16 Dimension Two and One Half -- 17 Dimension Three -- 18 Dimension Four -- Farewell -- Appendix -- References -- Index
  • 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.