Scaling Limit of Successive Approximations for w′=-w2

Tetsuya Hattori, Hiroyuki Ochiai

研究成果: Article査読

2 被引用数 (Scopus)

抄録

We prove existence of scaling limits of sequences of functions defined by the recursion relation w′n+1(ϰ)= -wn(ϰ)2. which is a successive approximation to w′(ϰ)= -wn(ϰ)2 a simplest non-linear ordinary differential equation whose solutions have moving singularities. Namely, the sequence approaches the exact solution as n→ √ in an asymptotically conformal way, [formula omitted], for a sequence of numbers {qn} and a function [formula omitted]. We also discuss implication of the results in terms of random sequential bisections of a rod.

本文言語English
ページ(範囲)291-319
ページ数29
ジャーナルFunkcialaj Ekvacioj
49
2
DOI
出版ステータスPublished - 2006
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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