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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 $\Bbb T ^1$. By lifting maps on $\Bbb T ^1$ and maps on the torus $\Bbb T ^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.

39B12Iterative and composite functional equations
39B32Functional equations for complex functions
39B82Stability, separation, extension, and related topics
37E05Maps of the interval (piecewise continuous, continuous, smooth)
Full Text: DOI EuDML
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