Nonlinear Dynamics and Chaos

  1. Hamiltonian Dynamics and Conservative Systems
    1. Hamiltonian Formalism
      1. Hamilton's Equations
        1. Phase Space Structure
          1. Conservation Laws
            1. Canonical Transformations
            2. Integrable Systems
              1. Action-Angle Variables
                1. Tori in Phase Space
                  1. Periodic and Quasiperiodic Motion
                  2. KAM Theory
                    1. KAM Theorem Statement
                      1. Breakdown of Integrability
                        1. Transition to Chaos
                        2. Poincaré Sections
                          1. Construction and Analysis
                            1. Fixed Points and Periodic Orbits
                              1. Chaotic Seas and KAM Tori
                              2. Examples of Hamiltonian Chaos
                                1. Standard Map
                                  1. Hénon-Heiles System
                                    1. Double Pendulum
                                      1. Billiard Systems

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                                    8. Fractal Geometry

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                                    10. Synchronization Phenomena