Explore the baker map and Arnold cat map — canonical ergodic systems. Watch phase space mixing as iterates fill the torus, observe ergodic averages converging to space averages, and measure Lyapunov exponents from exponential divergence of nearby orbits.
Baker map: (x,y)→(2x mod 1, y/2) if x<½, else (2x-1, (y+1)/2). Lyapunov exponent λ=ln2≈0.693.
Cat map: (x,y)→(x+y, x+2y) mod 1. Eigenvalues φ²=(3±√5)/2, λ=ln(φ²)≈0.962.
Birkhoff ergodic theorem: time avg = space avg for a.e. initial condition.