Probabilistic Control on Kicked Rotor

Chaotic systems can be probabilistically controlled onto unstable periodic orbits by coupling the stochastic action of the map and a control map. The resulting system exhibits controlled and uncontrolled phases, depending on the rate at which the control map is applied. We study the properties of control phase transition in the kicked rotor system. In our analysis, we characterize the transition using an order parameter and further probe it by calculating Lyapunov exponents.