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Böttcher's equation, named after Lucjan Böttcher, is the functional equation :: where * is a given analytic function with a superattracting fixed point of order at , (that is, in a neighbourhood of ), with ''n'' ≥ 2 * is a sought function. The logarithm of this functional equation amounts to Schröder's equation. ==Solution== Lucian Emil Böttcher sketched a proof in 1904 on the existence of an analytic solution ''F'' in a neighborhood of the fixed point ''a'', such that ''F''(''a'') = 0. This solution is sometimes called the ''Böttcher coordinate''. (The complete proof was published by Joseph Ritt in 1920, who was unaware of the original formulation.) Böttcher's coordinate (the logarithm of the Schröder function) conjugates in a neighbourhood of the fixed point to the function . An especially important case is when is a polynomial of degree , and = ∞ . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Böttcher's equation」の詳細全文を読む スポンサード リンク
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