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A general class of iterative equations on the unit circle. (English) Zbl 1174.39005
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.

##### MSC:
 39B12 Iteration theory, iterative and composite equations 39B32 Functional equations for complex functions 39B82 Stability, separation, extension, and related topics for functional equations 37E05 Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth)
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