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Friday, October 17, 2014

**Abstract:** Hamiltonian Systems are an intrinsic part of our world and appear in examples as basic as a simple pendulum, rotations on a sphere, and even the motion of a top. Of course, it is natural to ask when considering such examples: do these systems have solutions? We will consider Hamiltonian Systems where the answer to this question is yes, that is Completely Integrable Hamiltonian Systems. It turns out that the Arnold-Liouville Theorem gives us a characterization of the dynamics of such systems. Our goal will be to give a sketch of the proof assuming only basic knowledge of symplectic manifolds and differential topology.