Targeting unstable periodic orbits

Specific targeting of unstable periodic orbits has been achieved by using large-amplitude perturbations in a dynamical system. The method has been demonstrated experimentally on a ${\mathrm{CO}}_2$ laser with modulated losses whose unstable periodic orbits are created either at a period-doubling or at a saddle-node bifurcation. Applications of the technique to switch the phase of the dynamical motion, to set boundaries of basins of attraction, and to measure Floquet multipliers are discussed.