Lecture

Periodic Orbits of Hamiltonian Systems

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Description

This lecture covers the topic of periodic orbits of Hamiltonian systems, focusing on Morse theory, critical points, and Conley-Zehnder index. The instructor discusses the stability of periodic orbits and their applications in dynamical systems.

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In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact.

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