Abstract
In the first part of the paper it is shown that analytic mappings of the circumference, differing little from a rotation, whose rotation number is irrational and satisfies certain arithmetical requirements, may be carried into a rotation by an analytic substitution of variables. In the second part we consider the space of mappings of the circumference onto itself and the place occupied in this space by mappings of various types. We indicate applications to the investigation of trajectories on the torus and to the Dirichlet problem for the equation of the string.
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(2009). Small denominators. I. Mapping of the circumference onto itself. In: Givental, A., et al. Collected Works. Vladimir I. Arnold - Collected Works, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01742-1_10
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