Notes: Near-identity transformations to split fast and slow motion

The name near-identity transformation (NIT) is just shorthand for a specific application of perturbation theory—one which is particularly useful in dynamical systems that have slow and fast timescales. This is not all they can be used for (see e.g. Fumagalli+1 where a NIT is used to remove gauge dependence). What I write below is covered in some standard references but it’s easy enough to rederive…