Hamiltonian chaos: resonant driving creates an infinite stochastic web in phase space
Kick strength K0.5
Resonance q
Trajectories8
Iterations2000
The Zaslavsky web map is a Hamiltonian system with resonant driving. For resonance number q, the map
(x,p) → (x cos(2π/q) − (p+K sin x) sin(2π/q), x sin(2π/q) + (p+K sin x) cos(2π/q))
creates a stochastic web — a fractal network of chaotic channels filling phase space.
Between channels lie regular (KAM) regions. The web is self-similar with q-fold symmetry.
At small K, web channels are thin; as K increases, they widen until the KAM barriers are destroyed (Chirikov criterion).