The Kicked Rotator

The kicker rotator or standard map is a famous time discrete, nonlinear two-dimensional chaotic map governed by the equations:
\theta_{n+1}&=&\theta_{n}+p_{n+1}\quad\text{mod}\quad 2\pi
p_{n+1}&=&p_{n}+K\sin(\theta_n)\quad\text{mod}\quad 2\pi
When you click on a point in the phase plane below you select an initial condition for the angle and momentum variable, the map is iterated 1000 times and the trajectory is shown as dots with different colors for each run. You can also generate a set of traces for random initial conditions by clicking on the play button below. The constant K is a parameter, different values of which generate different dynamics. You can chose from a set of different K’s below.