# Article

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Keywords:
iterative equation; circle; lift; orientation-preserving; continuation
Summary:
A class of functional equations with nonlinear iterates is discussed on the unit circle ${\mathbb{T}}^1$. By lifting maps on ${\mathbb{T}}^1$ and maps on the torus ${\mathbb{T}}^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
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