2003 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(岡宏枝) 龍谷大学, 理工学部, 教授 (20215221) 四ツ谷晶二龍谷大学, 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	正則1型式 / Poincare-Hopfの定理 / Kacの問題 / 半線形楕円型方程式 / ホモクリニック軌道 / 分岐 / ニュートン法 / カントール族
Research Abstract	伊藤敏和はB.Scarduaとの共同研究で得られた結果「C^nのdiscの近傍で定義された正則1型式に対するPoincare-Hopf型定理」を次の国際会議(1)フランスの研究所CIRMでの「Web geometry and differential equations」,(2)ブラジルの研究所IMPAでの「Complex analytic methods in dynamical systems」,(3)龍谷大学での「Geometry and foliations 2003」で発表した。さらに,この結果をStein空間のある領域へ拡張した。松本和一郎は四ツ谷と村井との共同研究で最小曲率エネルギー曲線に囲まれる領域はKacの問題が肯定的な領域で,周長を固定して領域面積をSΠから小さくしていくと凸領域から凸でない領域に変わることを厳密に証明した。四ツ谷晶二はLou-NiとW.M.Niとの共同研究で未知定数を含む積分制約条件付きの半線形楕円型方程式の解の構造を研究するのに全く新しい方法を提案しそれを実行し,空間1次元の場合に,ほぼ完全な解答を与えた。森田善久はホモクリニック軌道をもつ常微分方程式系を2つ対称に結合した系を考え,対称な平衡点から新たな平衡点が分岐するとき,ホモクリニック軌道も分岐することを示した。山岸義和は二変数Newton法の重根のまわりの局所的な挙動を力学系の観点から調べ,二次収束する初期値の存在を示した。また緩和係数をつけた場合のニュートン法の重根の近傍においても,重根に対して速い収束をする初期値の集合が複素曲線のカントール族をなすことを示した。

Research Products

(13 results)

All Other

All Publications (13 results)

[Publications] T.Ito, B.Scardua: "On holomorphic one-forms transverse to closed hypersurfaces"Annals of Brazilian Academy of Sciences. 75-3. 265-269 (2003)
[Publications] T.Ito, B.Scardua: "Holomorphic foliations of codimension one transverse to polydiscs"J.fur die reine undangew.Math.. (to appear).
[Publications] T.Ito, B.Scardua: "A Poincare-Hopf type theorem for holomorphic one-forms"Topology. (to appear).
[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.. 145-156 (2003)
[Publications] W.Matsumoto, M.Murai, S.Yotsutani: "By which kind of sound, can one hear the shape of drum?"数理解析研究所講究録「波動現象と漸近解析」. 1315. 156-175 (2003)
[Publications] H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani: "On the global branches of the solutions to a nonlocal boundary-value problem arising in Ossen's spiral flows"Communication on Pure and Applied Analysis. 3-3. 381-390 (2003)
[Publications] E.Yanagida, S.Yotsutani: "Recent Topics on Nonlinear Partial Differential Equations : Structure of Radial Solutions for Semilinear Elliptic Equations"Amer.Math.Soc.Transl., Series. 2-211. 121-137 (2003)
[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. 10-1. 435-458 (2004)
[Publications] Y.Fukao, Y.Morita, H.Ninomiya: "Some entire solutions of the Allen-Cahn equation"Taiwanese J.Math.. (to appear).
[Publications] Y.Morita: "Stable Solutions to the Ginzburg-Londau Equation with Magnetic Effect in a Thin Domain"Japan J.Indust.Appl.Math.. (to appear).
[Publications] J.S.Guo, Y.Morita: "Entire solutions of rection-diffusion equations and an application to discrete diffusive equations"Discrete and Contin.Dynam.Systems. (to appear).
[Publications] Y.Yamagishi: "Quadratically convergent initial values to a double root in Newton's method of two variables"Progress in Analysis, proceedings of the 3rd ISAAC Congress (2003), World Scientific. 563-569 (2003)
[Publications] Y.Yamagishi: "On the local convergence of Newton's method to a multiple root"J.of the Math.Society of Japan. 55-4. 897-908 (2003)

2003 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] T.Ito, B.Scardua: "On holomorphic one-forms transverse to closed hypersurfaces"Annals of Brazilian Academy of Sciences. 75-3. 265-269 (2003)

[Publications] T.Ito, B.Scardua: "Holomorphic foliations of codimension one transverse to polydiscs"J.fur die reine undangew.Math.. (to appear).

[Publications] T.Ito, B.Scardua: "A Poincare-Hopf type theorem for holomorphic one-forms"Topology. (to appear).

[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.. 145-156 (2003)

[Publications] W.Matsumoto, M.Murai, S.Yotsutani: "By which kind of sound, can one hear the shape of drum?"数理解析研究所講究録「波動現象と漸近解析」. 1315. 156-175 (2003)

[Publications] H.Ikeda, K.Kondo, H.Okamoto, S.Yotsutani: "On the global branches of the solutions to a nonlocal boundary-value problem arising in Ossen's spiral flows"Communication on Pure and Applied Analysis. 3-3. 381-390 (2003)

[Publications] E.Yanagida, S.Yotsutani: "Recent Topics on Nonlinear Partial Differential Equations : Structure of Radial Solutions for Semilinear Elliptic Equations"Amer.Math.Soc.Transl., Series. 2-211. 121-137 (2003)

[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. 10-1. 435-458 (2004)

[Publications] Y.Fukao, Y.Morita, H.Ninomiya: "Some entire solutions of the Allen-Cahn equation"Taiwanese J.Math.. (to appear).

[Publications] Y.Morita: "Stable Solutions to the Ginzburg-Londau Equation with Magnetic Effect in a Thin Domain"Japan J.Indust.Appl.Math.. (to appear).

[Publications] J.S.Guo, Y.Morita: "Entire solutions of rection-diffusion equations and an application to discrete diffusive equations"Discrete and Contin.Dynam.Systems. (to appear).

[Publications] Y.Yamagishi: "Quadratically convergent initial values to a double root in Newton's method of two variables"Progress in Analysis, proceedings of the 3rd ISAAC Congress (2003), World Scientific. 563-569 (2003)

[Publications] Y.Yamagishi: "On the local convergence of Newton's method to a multiple root"J.of the Math.Society of Japan. 55-4. 897-908 (2003)

伊藤敏和龍谷大学, 経済学部, 教授 (60110178)