Nambu systems [@N]. A Hamiltonian system is a classical system described by a generalized coordinate $q=q(t)$ and its canonical conjugate momentum $p=p(t)$. These variables satisfy the Hamilton’s canonical equations of motion, $$\begin{aligned}
\frac{d q}{dt} = \frac{\partial H}{\partial p} ~,~~ \frac{d p}{dt} 
= -\frac{\partial H}{\partial q}~,
\label{H-eq}\end{aligned}$$ where $H=H(q, p)$ is the Hamiltonian of this system. For any functions $A=A(q,p,t)$ and $B=B(q,p,t)$, the Poisson bracket is defined by means of the 2-dimensional Jacobian, $$\begin{aligned}
\{A, B\}_{\mbox{\tiny{PB}}} \equiv  
\frac{\partial (A,B)}{\partial (q,p)}=
\frac{\partial A}{\partial q}\frac{\partial B}{\partial p}
 - \frac{\partial A}{\partial p}\frac{\partial B}{\partial q}~.
\label{PB}\end{aligned}$$ In terms of the Poisson bracket, the Hamilton’s canonical equation of motion for any function $f=f(p,q)$ can be written as $$\begin{aligned}
\frac{d f}{dt} = \{f, H\}_{\mbox{\tiny{PB}}}~.
\label{H-eqf}\end{aligned}$$

On the other hand, a Nambu system is a classical system described by a multiplet. As the most simple example, let us consider a Nambu system described by a triplet $x=x(t)$, $y=y(t)$, and $z=z(t)$. These variables satisfy the Nambu equations $$\begin{aligned}
\frac{d x}{dt} = \frac{\partial ({H}_1, {H}_2)}{\partial (y, z)}~,~~ 
\frac{d y}{dt} = \frac{\partial ({H}_1, {H}_2)}{\partial (z, x)}~,~~
\frac{d z}{dt} = \frac{\partial ({H}_1, {H}_2)}{\partial (x, y)}~,
\label{N-eq}\end{aligned}$$ where ${H}_1(x, y, z)$ and ${H}_2(x, y, z)$ are $\lq\lq$Hamiltonians" of this system. For any functions 