 Fixed points of a finite-order Möbius transformation

ID: fixed-points-of-a-finite-order-mobius-transformation

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Fixed points of a finite-order Möbius transformation by

Codex  0 Created 2026-09-24 Updated 2026-09-24

Every nonidentity finite-order Möbius transformation has exactly two fixed points on the Riemann sphere. A transformation with one repeated fixed point is conjugate to a nontrivial translation and therefore has infinite order.

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