オガワ　トシユキ   OGAWA Toshiyuki   小川　知之    所属   明治大学  総合数理学部    職種   専任教授
言語種別	日本語
発行・発表の年月	2005/12
形態種別	学術雑誌
査読	査読あり
標題	Rigorous numerics for global dynamics: A study of the swift-hohenberg equation
執筆形態	共著(筆頭者以外)
掲載誌名	SIAM Journal on Applied Dynamical Systems
掲載区分	国外
巻・号・頁	4,1-31頁
著者・共著者	Sarah Day, Yasuaki Hiraoka, Konstantin Mischaikow, Toshiyuki Ogawa
概要	This paper presents a rigorous numerical method for the study and verification of global dynamics. In particular, this method produces a conjugacy or semiconjugacy between an attractor for the Swift-Hohenberg equation and a model system. The procedure involved relies on first verifying bifurcation diagrams produced via continuation methods, including proving the existence and uniqueness of computed branches as well as showing the nonexistence of additional stationary solutions. Topological information in the form of the Conley index, also computed during this verification procedure, is then used to build a model for the attractor consisting of stationary solutions and connecting orbits. ? 2005 Society for Industrial and Applied Mathematics.
DOI	10.1137/040604479
ISSN	15360040
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