Chaos Theory: Turbulence and Double Pendulum

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Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Introduces equilibrium points and bifurcations in differential equations, discussing their stability and relevance in various contexts.

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Explores linear response for chaotic systems, discussing SRB states, Lyapunov exponents, and convergence of the response formula.

Explores chaos, irregular trajectories, and sensitivity to initial conditions in dynamical systems.

Delves into chaos and sensitivity in the double pendulum system, exploring unpredictability and exponential divergence of trajectories.

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Covers Morse theory, critical points, and Conley-Zehnder index in Hamiltonian systems.

Covers the dynamics of discrete systems and the concept of orbits in Riemann varieties.

Explores elements from Ergodic Theory, transformations, invariant sets, and Lyapunov Exponents for 1-dimensional maps.

Explores online gradient boosting for non-stochastic control problems, emphasizing policy regret minimization and stability in control.

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