Construction of approximate solutions for rigorous numerics of symmetric homoclinic orbits (Workshops on "Pattern Formation Problems in Dissipative Systems" and "Mathematical Modeling and Analysis for Nonlinear Phenomena")
Construction of approximate solutions for rigorous numerics of symmetric homoclinic orbits (Workshops on "Pattern Formation Problems in Dissipative Systems" and "Mathematical Modeling and Analysis for Nonlinear Phenomena")
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对称同宿轨道严格数值近似解的构造（“耗散系统中的模式形成问题”和“非线性现象的数学建模与分析”研讨会）
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发表时间：
2007
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通讯作者：
Y. Hiraoka
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作者：
Y. Hiraoka
通常是通过数值模拟得到的。在这种情况下，他给出了一种严格的数值方法来证明（1.1）的对称同斜轨道在数值解（1.2）的邻域内的存在性。我们参考原始论文[5]了解这项工作的背景和动机。在该方法中，根据显本质二分性，必须证明以下两个步骤：(i)在近似解w(t)， t\ In \ mathm {R}的邻域内原点稳定流形上轨道的存在性，这是确定的
which is usually obtained by numerical simulations. In this setting, he gives a rigorous numerical method to prove the existence of symmetric homoclinic orbits of (1.1) in a neighborhood of the numerical solution (1.2). We refer to the original paper [5] for the background and motivations of this work. In the method, it is essential to show the following two steps based on the expo‐ nential dichotomy property: (i) the existence of orbits on the stable manifold of the origin in a neighborhood of an approximate solution w(t) , t\in \mathrm{R} , which is determined