化工动力问题详解

     Contents
   CHAPTER1
    Introduction: Differential Equations and Dynamical Systems
    1.0. Existence and Uniqueness ofSolutions
    1.1. The Linear System x = Ax
    1.2. Flows and Invariant Subspaces
    1.3. The Nonlinear System x = f(x)
    1.4. Linear and Nonlinear Maps
    1.5. Closed Orbits. Poincare Maps and Forced Oscillations
    1.6. Asymptotic Behavior
    1.7. Equivalence Relations and Structural Stability
    1.8. Two-Dimensional Flows
    1.9. Peixoto's Theorem for Two-Dimensional Flows
   CHAPTER 2
    An Introduction to Chaos: Four Examples
    2.1. Van der Pol's Equation
    2.2. Duffing's Equation
    2.3. The Lorenz Equations
    2.4. The Dynamics ofa Bouncing Ball
    2.5. Conclusions: The Moral ofthe Tales
   CHAPTER 3
    Local Bifurcations
    3.1. Bifurcation Problems
    3.2. Center Manifolds
    3.3. Normal Forms
    3.4. Codimension One Bifurcations of Equilibria
    3.5. Codimension One Bifurcations ofMaps and Periodic Orbits
   CHAPTER 4
    Averaging and Perturbation from a Geometric Viewpoint
    4.1. Averaging and Poincare Maps
    4.2. Examples of Averaging
    4.3. Averaging and Local Bifureations
    4.4. Averaging, Hamiltonian Systems, and Global Behavior:
    Cautionary Notes
    4.5. Melnikov's Method: Perturbations ofPlanar Homoclinic Orbits
    4.6. Melnikov's Method: Perturbations of Hamiltonian Systems and
    Subharmonic Orbits
    4.7. Stability of Subharmonic Orbits
    4.8. Two Degree of Freedom Hamiltonians and Area Preserving Maps
    of the Plane
   CHAPTER 5
    Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors
    5.0. Introduction
    5.1. The Smale Horseshoe: An Example ofa Hyperbolic Limit Set
    5.2. Invariant Sets and Hyperbolicity
    5.3. Markov Partitions and Symbolic Dynamics
    5.4. Strange Attractors and the Stability Dogma
    5.5. Structurally Stable Attractors
    5.6. One-Dimensional Evidence for Strange Attractors
    5.7. The Geometric Lorenz Attractor
    5.8. Statistical Propenies: Dimension. Entropy and Liapunov Exponents
   CHAPTER 6
    Global Bifurcations
    6.1. Saddle Connections
    6.2. Rotation Numbers
    6.3. Bifurcations of One-Dimensional Maps
    6.4. The Lorenz Bifurcations
    6.5. Homoclinic Orbits in Three-Dimensional Flows: Silnikov's Example
    6.6. Homoclinic Bifurcations of Periodic Orbits
    6.7. Wild Hyperbolic Sets
    6.8. Renormalization and Universality
   CHAPTER7
    Local Codimension Two Bifurcations of Flows
    7.1. Degeneracy in Higher-Order Terms
    7.2. A Note on k-Sels and Determinacy
    7.3. The Double Zero Eigenvalue
    7.4. A Pure Imaginary Pair and a Simple Zero Eigenvalue
    7.5. Two Pure Imaginary Pairs of Eigenvalues without Resonance
    7.6. Applications to Large Systems
    APPENDIX
    Suggestions for Further Reading
    Postscript Added at Second Printing
    Glossary
    References
    Index