This video introduces chaotic dynamical systems, which exhibit sensitive dependence on initial conditions. These systems are ubiquitous in natural and engineering systems, from turbulent fluids to the motion of objects in the solar system. Here, we discuss how to recognize chaos and how to numerically integrate these systems.

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0:00 Overview of Chaotic Dynamics
8:49 Example: Planetary Dynamics
14:31 Example: Double Pendulum
19:12 Flow map Jacobian and Lyapunov Exponents
26:33 Symplectic Integration for Chaotic Hamiltonian Dynamics
33:41 Examples of Chaos in Fluid Turbulence
37:16 Synchrony and Order in Dynamics