# How do you define iterations of multivariable functions? To be clear(example): If

How do you define iterations of multivariable functions?
To be clear(example):
If $$\displaystyle{f}:\mathbb{R}^{{2}}\rightarrow\mathbb{R}$$
How do you define
$$\displaystyle{f}\circ{f},\text{or}{f}\circ\ldots\circ{f}?$$?

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accimaroyalde
The composition is undefined as
$$\displaystyle{f}\circ{f}=\mathbb{R}^{{2}}\rightarrow^{{f}}\mathbb{R}\rightarrow^{?}?.$$
However if you have a function $$\displaystyle\mathbb{R}^{{2}}\rightarrow^{{F}}\mathbb{R}^{{2}}$$, then we can easily form the composition.