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You can achieve this by

 sage: f.nth_iterate_map(2).defining_polynomials()
(x^4, y^4)


As a general tip, if you have an object that you want to get information out of, try assigning it to a variable e.g.

f2 = f.nth_iterate_map(2)


and then type f2.<TAB>; this will suggest a list of methods.