Dynamical Systems

1. Front Matter

   Pages i-xviii

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2. Introduction

   • Pierre N. V. Tu

   Pages 1-3

3. Review of Ordinary Differential Equations

   • Pierre N. V. Tu

   Pages 5-38

4. Review of Difference Equations

   • Pierre N. V. Tu

   Pages 39-57

5. Review of Some Linear Algebra

   • Pierre N. V. Tu

   Pages 59-82

6. First Order Differential Equations Systems

   • Pierre N. V. Tu

   Pages 83-114

7. First Order Difference Equations Systems

   • Pierre N. V. Tu

   Pages 115-131

8. Nonlinear Systems

   • Pierre N. V. Tu

   Pages 133-162

9. Gradient Systems, Lagrangean and Hamiltonian Systems

   • Pierre N. V. Tu

   Pages 163-181

10. Simplifying Dynamical Systems

    • Pierre N. V. Tu

    Pages 183-194

11. Bifurcation, Chaos and Catastrophes in Dynamical Systems

    • Pierre N. V. Tu

    Pages 195-243

12. Optimal Dynamical Systems

    • Pierre N. V. Tu

    Pages 245-269

13. Some Applications in Economics and Biology

    • Pierre N. V. Tu

    Pages 271-294

14. Back Matter

    Pages 295-315

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The favourable reception of the first edition and the encouragement received from many readers have prompted the author to bring out this new edition. This provides the opportunity for correcting a number of errors, typographical and others, contained in the first edition and making further improvements. This second edition has a new chapter on simplifying Dynamical Systems covering Poincare map, Floquet theory, Centre Manifold Theorems, normal forms of dynamical systems, elimination of passive coordinates and Liapunov-Schmidt reduction theory. It would provide a gradual transition to the study of Bifurcation, Chaos and Catastrophe in Chapter 10. Apart from this, most others - in fact all except the first three and last chapters - have been revised and enlarged to bring in some new materials, elaborate some others, especially those sections which many readers felt were rather too concise in the first edition, by providing more explana­ tion, examples and applications. Chapter 11 provides some good examples of this. Another example may be found in Chapter 4 where the review of Linear Algebra has been enlarged to incorporate further materials needed in this edition, for example the last section on idempotent matrices and projection would prove very useful to follow Liapunov-Schmidt reduction theory presented in Chapter 9.

• Differentialgleichungen
• Dynamical system
• algebra
• catastrophe theory
• differential equations
• dynamical systems
• dynamics
• dynamische Systeme
• economics
• nonlinear systems

"This book is the most useful recent review of differential equation systems that I have seen. The exposition is clear, explicit and accurate. It strikes an effective balance between rigor and readability, arguing proofs for the simpler cases, but citing publications for the more complex." The Quarterly Review of Biology

• Department of Economics, The University of Calgary, Calgary, Canada

  Pierre N. V. Tu

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