Approaches to the qualitative theory of ordinary differential equations : dynamical systems and nonlinear oscillations /
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| Author / Creator: | Ding, Tong-Ren. |
|---|---|
| Imprint: | New Jersey : World Scientific, c2007. |
| Description: | ix, 383 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Peking University series in mathematics ; v. 3 Peking University series in mathematics ; v. 3. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6652499 |
Table of Contents:
- Preface
- Chapter 1. Cauchy Problem
- 1.1. Fundamental Theorems
- 1.2. Method of Euler Polygons
- 1.3. Local Behavior of Integral Curves
- 1.4. Peano Phenomenon
- 1.5. Convergence Theorem on Difference Methods
- Chapter 2. Global Behavior of Solution
- 2.1. Global Existence of Solution
- 2.2. Predictability of Solution
- 2.3. Liapunov Stability
- 2.4. Liapunov Unstability
- Chapter 3. Autonomous Systems
- 3.1. Phase Portrait
- 3.2. Orbital Box
- 3.3. Types of Orbits
- 3.4. Singular Points
- 3.5. General Property of Singular Points
- 3.6. Closed Orbit
- 3.7. Invariant Torus
- 3.8. Limit-Point Set
- 3.9. Poincare-Bendixson Theorem
- Chapter 4. Non-Autonomous Systems
- 4.1. General Systems
- 4.2. Conservative Systems
- 4.3. Dissipative Systems
- 4.4. Planar Periodic Systems
- 4.5. Invariant Continuum
- Chapter 5. Dynamical Systems
- 5.1. The Originality
- 5.2. Recurrence
- 5.3. Quasi-Minimal Set
- 5.4. Minimal Set
- 5.5. Almost Periodic Motion
- Chapter 6. Fixed-Point Theorems
- 6.1. Poincare Index
- 6.2. Vector Fields on Closed Surfaces
- 6.3. Spatial Vector Fields
- 6.4. Fixed-Point Theorems of Brouwer Type
- Chapter 7. Bend-Twist Theorem
- 7.1. Generalized Poincare-Birkhoff Twist Theorem
- 7.2. Analytic Bend-Twist Theorem
- 7.3. Analytic Poincare-Birkhoff Twist Theorem
- 7.4. Application of the Bend-Twist Theorem
- Chapter 8. Chaotic Motions
- 8.1. Definition of Chaotic Motion
- 8.2. Chaotic Quasi-Minimal Set
- 8.3. Sufficient Conditions for Chaotic Sets
- 8.4. Chaotic Closed Surfaces
- 8.5. Applications
- Chapter 9. Perturbation Method
- 9.1. Nonlinear Differential Equation of Second Order
- 9.2. Method of Averaging
- 9.3. High Frequency Forced Oscillations
- Chapter 10. Duffing Equations of Second Order
- 10.1. Periodic Oscillations
- 10.2. Time-Map
- 10.3. Duffing Equation of Super-Linear Type
- 10.4. Duffing Equation of Sub-Linear Type
- 10.5. Duffing Equation of Semi-Linear Type
- Chapter 11. Some Special Problems
- 11.1. Reeb's Problem
- 11.2. Birkhoff's Conjecture
- 11.3. Morse's Conjecture
- 11.4. Kolmogorov's Problem
- 11.5. Brillouin Focusing System
- 11.6. A Retarded Equation
- 11.7. Periodic Lotka-Volterra System
- Bibliography
