The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with stochastic resetting drives a sharp dynamical phase transition: we show that the Lyapunov spectrum, i.e., the complete set of Lyapunov exponents, abruptly collapses to zero above a critical resetting rate. At criticality, we find a sudden loss of analyticity of the velocity-dependent Lyapunov exponent, which we relate to the transition from ballistic scrambling of information to an arrested regime where information becomes exponentially localized over a characteristic length diverging at criticality with an exponent $\nu =1/2$ and a dynamical exponent $z=2$. We illustrate our analytical results on generic chaotic dynamics by numerical simulations of coupled map lattices.

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• Chaos
• Dynamical phase transitions
• Spatiotemporal chaos
• Stochastic resetting
• Chaotic systems
• Collective dynamics
• Dynamical systems
• Stochastic dynamical systems
• Chaos & nonlinear dynamics