Nonlinear Dynamics and Chaos
Hamilton's Equations
Phase Space Structure
Conservation Laws
Canonical Transformations
Action-Angle Variables
Tori in Phase Space
Periodic and Quasiperiodic Motion
KAM Theorem Statement
Breakdown of Integrability
Transition to Chaos
Construction and Analysis
Fixed Points and Periodic Orbits
Chaotic Seas and KAM Tori
Standard Map
Hénon-Heiles System
Double Pendulum
Billiard Systems
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8. Fractal Geometry
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10. Synchronization Phenomena