1変数複素有理反復法の収束範囲の形状について

概要

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Starting from the properties of invariant figures for a rational function of a complex variable, the global features of rational iterations treated by Julia, Fatou etc, are reviewed briefly, and some new theorems about the areas of convergence useful for their numerical tracing are derived. The domain of direct convergence in Julia's sense is a component of the largest open "minimal invariant figure", contained in the whole area of convergence whose limit is a stable or semistable fixed point. It is shown that, in most cases of practical importance, the domain itself is also minimal invariant and its boundary contains a minimal invariant figure on which unstable fixed points and their antecedents are arranged in a simple manner. The configuration of convergence areas can be traced with practically sufficient accuracy, by numerically calculating all fixed points and their several antecedents.
一般社団法人情報処理学会の論文
1978-08-15