Periodic Orbits of Hamiltonian Systems

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Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Explores compact sets, extreme values, and function theorems on bounded sets.

Explores periodic orbits in Hamiltonian systems and their stability under various conditions.

Explores the problem of a falling stone hitting the moon, focusing on gateways to the moon and local Floer homology.

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Explores adhesion, convergence, closed sets, compact subsets, and examples of subsets in R^n.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Covers extreme values of continuous functions on compact sets and differentiability.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Explores small scale stability in gradient systems, analyzing trajectories and attractors in phase space.