Studies of differential equations in dynamical systems view by means of geometric and topological methods

2013 Fiscal Year Final Research Report

• Project/Area Number: 21540221
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kyushu University
• Principal Investigator: NII Shunsaku 九州大学, 数理(科)学研究科(研究院), 准教授 (50282421)
• Project Period (FY): 2009-04-01 – 2014-03-31
• Keywords: Stability Index / 分岐 / 幾何学的方法 / 位相的方法

Research Abstract

(1)Differential equations were studied in dynamical systems view, especially, homoclinic and heteroclinic bifurcations and bifurcations and stability of traveling waves, in reaction diffusion equations in which those bifurcations naturally appear, were treated by means of geometric and topological methods. Infinite dimensional Stability Indices and infinite dimensional Maslov Indices were focused.
(2)Bifurcation analysis were carried in which the systems were assumed to be completely degenerate. Those were contrary to standard bifurcation theory in which the systems are assumed to be non-degenerate and singular points are classified.