Nonlinear Dynamics and Chaos

  1. Fractal Geometry
    1. Introduction to Fractals
      1. Definition and Characteristics
        1. Self-Similarity
          1. Scale Invariance
            1. Fractal vs. Euclidean Geometry
            2. Fractal Dimension
              1. Hausdorff Dimension
                1. Box-Counting Dimension
                  1. Correlation Dimension
                    1. Information Dimension
                      1. Generalized Dimensions
                      2. Classical Fractals
                        1. Cantor Set
                          1. Construction
                            1. Measure and Dimension
                            2. Sierpinski Triangle
                              1. Koch Snowflake
                                1. Dragon Curve
                                  1. Menger Sponge
                                  2. Random Fractals
                                    1. Brownian Motion
                                      1. Fractional Brownian Motion
                                        1. Percolation Clusters
                                        2. Fractals in Dynamical Systems
                                          1. Julia Sets
                                            1. Definition and Construction
                                              1. Filled Julia Sets
                                                1. Connection to Dynamics
                                                2. Mandelbrot Set
                                                  1. Definition in Parameter Space
                                                    1. Relationship to Julia Sets
                                                      1. Self-Similarity and Universality
                                                      2. Fractal Basin Boundaries
                                                        1. Strange Attractors as Fractals

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                                                      7. Universality and Scaling

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                                                      9. Hamiltonian Dynamics and Conservative Systems