If f and g are Mobius Transformations, why does this hold?
$$gf^{n}g^{-1}(z)=z+n$$ implies $$f^{n}(z)=g^{-1}(g(z)+n) $$
2026-03-28 11:42:15.1774698135
Quick question on Mobius Transformation Iteration
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Hint: Try substituting $g(w)$ for $z$ in your first equation, and then do everything you can to simplify and get an expression for $f^n(w)$.
(Then you can replace $w$ with any other symbol you like...such as $z$.)