Periodic Orbits of Hamiltonian Systems

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Explores compact subsets of R^n, convergence theorems, and set properties.

Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Discusses separation conditions, graph, and saturations in equivalence relations on a space.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Discusses open subsets, compact sets, and methods for demonstrating openness in a space.

Explores linear operations, convergence, sequences, and compact sets in mathematical analysis.

Delves into Chaos Theory, exploring chaotic systems, sensitivity to initial conditions, and the dynamics of the double pendulum.

Covers the properties of closed sets and their convergence within subsequences.

Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.