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AuthorHale, Jack K. author
TitleDynamics and Bifurcations [electronic resource] / by Jack K. Hale, Hรผseyin Koรงak
ImprintNew York, NY : Springer New York, 1991
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Descript XIV, 574 p. online resource


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


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

Mathematics Mathematical analysis Analysis (Mathematics) Statistical physics Dynamical systems Mathematics Analysis Statistical Physics Dynamical Systems and Complexity


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