Chaos Theory: Logistic Map and Periodic Orbits

This lecture covers Chaos Theory, focusing on the logistic map and periodic orbits. Topics include sensitivity to initial conditions, topological mixing, Lyapunov exponents, Feigenbaum scenario, and stability conditions for different values of the logistic map parameter. The instructor explains the concept of fix points, linear stability, and the transition to chaos. The lecture also delves into chaotic maps, fractal dimensions, and the period doubling cascade, illustrating the Feigenbaum scenario. Additionally, the discussion extends to intermittent chaos, Pomeau-Manneville scenario, and the computation of Lyapunov exponents for conjugate maps.