How do I patch sections of polyurethane coating on a hardwood floor?
I have had repairs done on oak floors that resulted in refinishing small areas.  It looks remarkably good.  The process is straightforward: sand the area, clean it with a solvent afterwards (denatured alcohol), apply polyurethane, let dry.

Use solvent based polyurethane and get the same finish type (gloss, satin, etc.) and apply a few thick coats.