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Physics
Applied and Interdisciplinary Physics
Nonlinear Dynamics and Chaos
1. Introduction to Dynamical Systems
2. One-Dimensional Flows
3. Two-Dimensional Flows
4. Higher-Dimensional Systems
5. Introduction to Chaos in Continuous Systems
6. Discrete Dynamical Systems and Maps
7. Universality and Scaling
8. Fractal Geometry
9. Hamiltonian Dynamics and Conservative Systems
10. Synchronization Phenomena
11. Control of Chaos
12. Spatiotemporal Dynamics
13. Time Series Analysis
14. Applications in Physical Sciences
15. Applications in Life Sciences
16. Applications in Chemistry
17. Applications in Engineering
18. Applications in Economics and Social Sciences
19. Computational Methods
9.
Hamiltonian Dynamics and Conservative Systems
9.1.
Hamiltonian Formalism
9.1.1.
Hamilton's Equations
9.1.2.
Phase Space Structure
9.1.3.
Conservation Laws
9.1.4.
Canonical Transformations
9.2.
Integrable Systems
9.2.1.
Action-Angle Variables
9.2.2.
Tori in Phase Space
9.2.3.
Periodic and Quasiperiodic Motion
9.3.
KAM Theory
9.3.1.
KAM Theorem Statement
9.3.2.
Breakdown of Integrability
9.3.3.
Transition to Chaos
9.4.
Poincaré Sections
9.4.1.
Construction and Analysis
9.4.2.
Fixed Points and Periodic Orbits
9.4.3.
Chaotic Seas and KAM Tori
9.5.
Examples of Hamiltonian Chaos
9.5.1.
Standard Map
9.5.2.
Hénon-Heiles System
9.5.3.
Double Pendulum
9.5.4.
Billiard Systems
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8. Fractal Geometry
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10. Synchronization Phenomena