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Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

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§11. Cremer Points and Siegel Disks

Once more we consider maps of the form

image

which are defined and holomorphic throughout some neighborhood of the origin, with a fixed point of multiplier λ at the origin. In §§8 and 9 we supposed that |λ| ≠ 1, while in §10 we took λ to be a root of unity. This section considers the remaining cases where |λ| = 1 but λ is not a root of unity. Thus we assume that the multiplier λ can be written as

image

Briefly, we will say that the origin is an irrationally indifferent fixed point. The number ξ / is called the rotation ...

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