Nonlinear Dynamics and Chaos

  1. Higher-Dimensional Systems
    1. Three-Dimensional Flows
      1. Phase Space Structure
        1. Types of Attractors
          1. Stable and Unstable Manifolds
            1. Heteroclinic and Homoclinic Connections
            2. Hyperbolic Systems
              1. Definition of Hyperbolicity
                1. Stable and Unstable Subspaces
                  1. Structural Stability
                  2. Center Manifold Theory
                    1. Center Manifold Theorem
                      1. Reduction to Center Manifold
                        1. Applications to Bifurcation Analysis

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                      3. Two-Dimensional Flows

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                      5. Introduction to Chaos in Continuous Systems