2001 Fiscal Year Annual Research Report

余次元1正則葉層構造に対するPoincare-Bendixson型定理とその応用

Research Project

Project/Area Number	13640092
Research Institution	Ryukoku University
Principal Investigator	伊藤敏和龍谷大学, 経済学部, 教授 (60110178)
Co-Investigator(Kenkyū-buntansha)	国府宏枝龍谷大学, 理工学部, 教授 (20215221) 四ッ谷晶二龍谷大学, 理工学部, 教授 (60128361) 松本和一郎龍谷大学, 理工学部, 教授 (40093314) 山岸義和龍谷大学, 理工学部, 助手 (40247820) 森田善久龍谷大学, 理工学部, 教授 (10192783)
Keywords	複素葉層構造 / 複素力学系 / 半線形楕円型方程式 / 共形スカラー曲率方程式 / ホモクリニック分岐 / 特異極限 / 周期的不定点 / 南雲型Cauchy-Kowalevskaya定理
Research Abstract	伊藤敏和は2001年4月14日〜16日に龍谷大学で「複素葉層構造と複素力学系」研究集会を開催し、この講義録(英語で)を作製した。得られた成果を国際会議「Foliation and Geometry 2001」(2001年8月2日〜11日,リオ・デ・ジャネイロ)で発表した。四ッ谷晶二は柳田氏との共同研究で半線形楕円型方程式の正値球対称解の標準形理論を作り,それを特異解の構造解明と共形スカラー曲率方程式に応用し,いくつもの成果を得た。松本和一郎は山原氏との共同研究で,係数が解析的な単独高階偏微分方程式の解析的初期値に対する初期値問題の必要十分条件をサイズが2の系で空間次元が1の時に肯定的に解決した。森田善久はホモクリニック軌道をもつ常微分方程式を対称的に結合したとき,非対称な1組のホモクリニック軌道が分岐する条件を明らかにし,具体的な例でその条件を確めた。ギンツブルグ・ランダウ方程式における特異極限で渦系の運動を表わす極限方程式を導き,その平衡解の構造や,渦系の消滅について解析した。山岸義和は射影平面上の有理写像で定義された力学系における周期的な不定点が一定の条件の下で安定多様体のカントール族をもつことを調べた。またこの応用として,2変数ニュートン法における階数1の重根が一定の条件の下で,2次収束する初期値をもつことを調べた。さらに,これらの力学系に摂動を与えたときの安定多様体の存在について調べた。

Research Products

(11 results)

All Other

All Publications (11 results)

[Publications] Y.Yamagishi: "Cantor bouquet of holomorphic stable manifolds for a periodec indeterminate point"Nonlinearity. 14. 113-120 (2001)
[Publications] T.Ito: "Some examples and problems of contact sets (polar varieties) of spheres and holomorphic vector fields"The Ryukoku Journal of Humanities and Sciences. 22-2. 145-152 (2001)
[Publications] H.Morishita, E.Yanagida, S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14-3. 273-288 (2001)
[Publications] E.Yanagida, S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan J. Indust. Appl. Math.. 18-2. 503-519 (2001)
[Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball"Proc. Roy. Soc. Edinburgh Sect. A. 131-3. 647-665 (2001)
[Publications] S.Yotsutani: "Canonical form related with radial solutions of semilinear elliptic equations and its apllications"Taiwanese J. Math.. 5-3. 507-517 (2001)
[Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communication on Pure and Applied Analysis. 1(to appear). (2002)
[Publications] Y.Lou, W.M.Ni, S.Yotsutani: "On a limiting system in the Lotka-Volterra competition with cross-diffusion"Discrete and Continuous Dynamical Systems. (to appear). (2002)
[Publications] W.Matsumoto, M.Murai, T.Nagase: "On the Cauchy-Kowalevskaya theorem of Nagumo type for systems"Hyperbolic differential operators and related problems, ed. V. Ancina et al., Marcel Dekker. (to appear).
[Publications] Y.Morita, J.Dookery, M.Pernarowski: "Symmetry Breaking homoclinic bifurcations in difurcations in diffusively coupled equations"J. Dynamics and Differential Equations. 13. 613-649 (2001)
[Publications] S.Jimbo, Y.Morita: "Notes on the limit equation of Vortex Motion for the Ginzburg-Landou equation with Neumann condition"Japan J. Indust, Appl. Math.. 18. 483-501 (2001)

2001 Fiscal Year Annual Research Report

余次元1正則葉層構造に対するPoincare-Bendixson型定理とその応用

Principal Investigator

伊藤 敏和 龍谷大学, 経済学部, 教授 (60110178)

Research Products

[Publications] Y.Yamagishi: "Cantor bouquet of holomorphic stable manifolds for a periodec indeterminate point"Nonlinearity. 14. 113-120 (2001)

[Publications] T.Ito: "Some examples and problems of contact sets (polar varieties) of spheres and holomorphic vector fields"The Ryukoku Journal of Humanities and Sciences. 22-2. 145-152 (2001)

[Publications] H.Morishita, E.Yanagida, S.Yotsutani: "Structural change of solutions for a scalar curvature equation"Differential and Integral Equations. 14-3. 273-288 (2001)

[Publications] E.Yanagida, S.Yotsutani: "A unified approach to the structure of radial solutions for semilinear elliptic problems"Japan J. Indust. Appl. Math.. 18-2. 503-519 (2001)

[Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball"Proc. Roy. Soc. Edinburgh Sect. A. 131-3. 647-665 (2001)

[Publications] S.Yotsutani: "Canonical form related with radial solutions of semilinear elliptic equations and its apllications"Taiwanese J. Math.. 5-3. 507-517 (2001)

[Publications] Y.Kabeya, E.Yanagida, S.Yotsutani: "Canonical forms and structure theorems for radial solutions to semi-linear elliptic problems"Communication on Pure and Applied Analysis. 1(to appear). (2002)

[Publications] Y.Lou, W.M.Ni, S.Yotsutani: "On a limiting system in the Lotka-Volterra competition with cross-diffusion"Discrete and Continuous Dynamical Systems. (to appear). (2002)

[Publications] W.Matsumoto, M.Murai, T.Nagase: "On the Cauchy-Kowalevskaya theorem of Nagumo type for systems"Hyperbolic differential operators and related problems, ed. V. Ancina et al., Marcel Dekker. (to appear).

[Publications] Y.Morita, J.Dookery, M.Pernarowski: "Symmetry Breaking homoclinic bifurcations in difurcations in diffusively coupled equations"J. Dynamics and Differential Equations. 13. 613-649 (2001)

[Publications] S.Jimbo, Y.Morita: "Notes on the limit equation of Vortex Motion for the Ginzburg-Landou equation with Neumann condition"Japan J. Indust, Appl. Math.. 18. 483-501 (2001)

伊藤敏和龍谷大学, 経済学部, 教授 (60110178)