Chaotic systems 6 Lyapunov decay 6 External perturbations 4 Fidelity amplitude 4 Quantum chaotic systems 4 Random dynamics 4 Random perturbations 4 Semiclassical approaches 4 Semiclassical theories 4 Cat map 2 Coherent oscillations 2 Decay (organic) 2 Decay rate 2 Differential equations 2 Local density of state 2 Local perturbation 2 Loschmidt echoes 2 Lyapunov exponent 2 Nonuniform 2 Perturbation strength 2 Phase space methods 2 Phase spaces 2 Quantum evolution 2 Small region 2 Weak perturbation 2