In the theory of

dynamical systems In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

(or

turbulent flow In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by Chaos theory, chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disrupt ...

), the Pomeau–Manneville scenario is the transition to chaos (turbulence) due to

intermittency In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics ( Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency). Experimentally ...

. Named after

Yves Pomeau Yves Pomeau, born in 1942, is a French mathematician and physicist, emeritus research director at the French National Centre for Scientific Research, CNRS and corresponding member of the French Academy of Sciences, French Academy of sciences. He w ...

and Paul Manneville. The aforementioned scenario is realized using the Pomeau–Manneville map. The Pomeau–Manneville map is a polynomial mapping (equivalently, recurrence relation), often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. Unlike other maps, the Pomeau–Manneville map exhibits

, characterized by periods of low and high amplitude fluctuations. Recent research suggests that this bursting behavior might lead to anomalous diffusion.

References

Dynamical systems Chaos theory Turbulence {{chaos-stub