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Ushiki's theorem
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Ushiki's theorem : ウィキペディア英語版
Ushiki's theorem
In mathematics, particularly in the study of functions of several complex variables, Ushiki's theorem, named after S. Ushiki, states that certain well-behaved functions cannot have certain kinds of well-behaved invariant manifolds.
== The theorem ==
A biholomorphic mapping F:\mathbb^n\to\mathbb^n can not have a 1-dimensional compact smooth invariant manifold. In particular, such a map cannot have a homoclinic connection or heteroclinic connection.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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