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Periodic orbits in Hamiltonian systems
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Classroom Contents
Stability of Periodic Orbits - Floquet Theory - Stable and Unstable Invariant Manifolds
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- 1 State transition matrix introduction
- 2 State transition matrix for periodic orbit (monodromy matrix)
- 3 Stability of the periodic orbit from monodromy matrix eigenvalues
- 4 Floquet multipliers, characteristic multipliers
- 5 Example scenarios in 3D
- 6 Saddle-type periodic orbit with stable and unstable manifolds
- 7 Periodic orbits in Hamiltonian systems
- 8 Example scenarios for 3 degrees of freedom (6D phase space)
- 9 Chaos in Hamiltonian systems, introduction via Duffing system
