Pomeau–Manneville scenario

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The Pomeau–Manneville scenario explains how chaos can begin in simple dynamical systems through intermittency, the pattern of long calm intervals punctuated by short bursts of activity. Named after Yves Pomeau and Paul Manneville, it is often illustrated with the Pomeau–Manneville map, a simple nonlinear rule that shows both steady behavior and chaotic bursts. This intermittent behavior helps explain how turbulence can arise in fluid flows. The bursts can lead to anomalous diffusion, a spreading process that does not follow ordinary diffusion laws. The scenario is a key concept in the study of the transition to turbulence in dynamical systems.