##  [Koopman Operator](/koopman-operator) 

  ##  [Koopman Operator](https://natural.quantumdictionary.io/koopman-operator-0) 

  

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Definition

The linear (often infinite-dimensional) operator U that advances observables of a dynamical system by composition with the flow or map: (U g)(x)=g(f(x)) for a discrete map x↦f(x) or (U^t g)=g∘Φ^t for continuous flow Φ^t; it encodes nonlinear state evolution as linear action on functions of state.