Nonlinear Dynamics and Chaos

  1. Discrete Dynamical Systems and Maps
    1. One-Dimensional Maps
      1. Basic Concepts
        1. Iteration and Orbits
          1. Fixed Points and Periodic Points
            1. Graphical Analysis (Cobweb Plots)
            2. The Logistic Map
              1. Mathematical Formulation
                1. Parameter Dependence
                  1. Fixed Point Analysis
                    1. Period-Doubling Cascade
                      1. Chaotic Regime
                        1. Symbolic Dynamics
                        2. Other Important Maps
                          1. Tent Map
                            1. Shift Map
                              1. Circle Map
                                1. Quadratic Family
                              2. Stability and Bifurcations in Maps
                                1. Linear Stability Analysis
                                  1. Period-Doubling Bifurcations
                                    1. Tangent Bifurcations
                                      1. Flip Bifurcations
                                      2. Routes to Chaos
                                        1. Period-Doubling Route
                                          1. Feigenbaum Scenario
                                            1. Universal Constants
                                            2. Intermittency
                                              1. Type I Intermittency
                                                1. Type II Intermittency
                                                  1. Type III Intermittency
                                                  2. Quasiperiodic Route
                                                    1. Circle Maps
                                                      1. Mode Locking
                                                        1. Arnold Tongues
                                                      2. Two-Dimensional Maps
                                                        1. The Hénon Map
                                                          1. Mathematical Definition
                                                            1. Parameter Space
                                                              1. Chaotic Attractors
                                                              2. Standard Map
                                                                1. Physical Context
                                                                  1. KAM Theory
                                                                    1. Chaos and Integrability
                                                                    2. Baker's Map
                                                                      1. Horseshoe Map

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                                                                    5. Introduction to Chaos in Continuous Systems

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                                                                    7. Universality and Scaling