An introduction to dynamical systems : continuous and discrete
著者
書誌事項
An introduction to dynamical systems : continuous and discrete
Pearson Prentice Hall, c2004
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注記
Includes bibliographical references (p. 641-645) and index
内容説明・目次
内容説明
For one- or two-semester courses in Dynamical Systems in the department of Advanced Mathematics.
This text gives an introduction into the ideas of dynamical systems. It is divided into two parts which can be treated in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit. The text assumes that students have taken courses on calculus covering both a single variable and multivariables, a course on linear algebra, and an introductory course on differential equations.
目次
(NOTE: Each chapter concludes with Applications, Theory and Proofs, and Exercises.)
Prologue: Historical Perspective.
I. SYSTEMS OF DIFFERENTIAL EQUATIONS.
1. Geometric Approach to Differential Equations.
2. Linear Systems.
3. The Flow: Solutions of Nonlinear Equations.
4. Phase Portraits with Emphasis on Fixed Points.
5. Phase Portraits Using Energy and Other Test Functions.
6. Periodic Orbits.
7. Chaotic Attractors.
II. ITERATION OF FUNCTIONS.
8. Iteration of Functions as Dynamics.
9. Periodic Points of One-Dimensional Maps.
10. Itineraries for One-Dimensional Maps.
11. Invariant Sets for One-Dimensional Maps.
12. Periodic Points of Higher Dimensional Maps.
13. Invariant Sets for Higher Dimensional Maps.
14. Fractals.
Appendix A: Calculus Background.
Appendix B: Analysis and Topology Terminology.
Appendix C: Linear Algebra Background.
Bibliography.
Index.
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