This course covers the stability of periodic orbits and invariant manifolds in Hamiltonian and nonlinear dynamics. Students will learn about the monodromy matrix, Floquet multipliers, and the relationship between the monodromy matrix eigenvalues and stability. The course includes examples in 3D, discussions on saddle-type periodic orbits, and chaos in Hamiltonian systems. The teaching method involves lectures with detailed explanations and examples. This course is intended for graduate students studying advanced dynamics, nonlinear dynamics, and dynamical systems.
Stability of Periodic Orbits - Floquet Theory - Stable and Unstable Invariant Manifolds
Overview
Syllabus
State transition matrix introduction.
State transition matrix for periodic orbit (monodromy matrix).
Stability of the periodic orbit from monodromy matrix eigenvalues.
Floquet multipliers, characteristic multipliers.
Example scenarios in 3D.
Saddle-type periodic orbit with stable and unstable manifolds.
Periodic orbits in Hamiltonian systems.
Example scenarios for 3 degrees of freedom (6D phase space).
Chaos in Hamiltonian systems, introduction via Duffing system.
Taught by
Ross Dynamics Lab
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