Dynamics and bifurcations

In recent years, due primarily to the proliferation of computers, dynamical systems has again returned to its roots in applications. It is the aim of this book to provide undergraduate and beginning graduate students in mathematics or science and engineering with a modest foundation of knowledge. 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. Further, the authors investigate the dynamics of planar autonomous equations where new dynamical behavior, such as periodic and homoclinic orbits appears.

Part I: Dimension One * Chapter 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

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