Nambu-Hamiltonian Flows Associated with Discrete Maps

Abstract

For a differentiable map (x₁,x₂,…,x_n)→(X₁,X₂,…,X_n) that has an inverse, we show that there exists a Nambu-Hamiltonian flow in which one of the initial value, say x_n, of the map plays the role of time variable while the others remain fixed. We present various examples which exhibit the map–flow correspondence.