The following is the standard notation for function composition of a single variable: $(f\circ g)(x)=f(g(x))$.
But is there common notation for the following: $f_1(f_2(x,y_1),y_2)$ when I have $N$ such functions? Here, $f_n: \mathbf{R}^3 \times \{1,2,3\} \rightarrow \mathbf{R}^3 \times \{1,2,3\}$.