This video is not stand-alone, but accompanies the free textbook at https://github.com/pbienst/active-math Background photo created by topntp26 - www.freepik.com
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The Lorenz attractor
Continuous systems
Phase portraits
Stable and unstable manifold
Non-linear maps and the Jacobian matrix
Stability of linear maps
Saddle points
2D maps - Henon
Sensitive dependence on initial conditions
Family of logistic maps
Periodic points
Stability theorem for fixed points
Sinks and sources
Cobweb diagrams
1D maps and logistic growth
Dynamical systems
Chaos in a photonic system
Photonic crystals
Square lattice of dielectric rods
The irreducible Brillouin zone
The Brillouin zone in 3D
Two metal plates and a dielectric walk into a bar...
Fun with commutators
EX: Second form of Bloch's theorem in 3D