论文标题
有关中心歧管的参数化方法的更多信息
More on the parameterization method for center manifolds
论文作者
论文摘要
在上一篇论文中，我们将Cabré，Fontich和de la Llave的参数化方法推广到离散动力学系统的中心歧管。在本文中，我们将此结果扩展到几个不同的设置。发生中心歧管的自然环境是在具有参数的动态系统中分叉。我们的第一个结果将表明，我们可以在分叉点附近找到参数依赖的中心歧管。此外，我们将将参数化方法推广到ODE的固定点的中心歧管。最后，我们将我们的方法应用于反应扩散方程。在我们的应用程序中，我们将证明以正常形式获得共轭动态的自由使得获得有关中心动态的详细定性信息成为可能。
In a previous paper we generalized the parameterization method of Cabré, Fontich and De la Llave to center manifolds of discrete dynamical systems. In this paper, we extend this result to several different settings. The natural setting in which center manifolds occur is at bifurcations in dynamical systems with parameters. Our first results will show that we can find parameter-dependent center manifolds near bifurcation points. Furthermore, we will generalize the parameterization method to center manifolds of fixed points of ODEs. Finally, we will apply our method to a reaction diffusion equation. In our application, we will show that the freedom to obtain the conjugate dynamics in normal form makes it possible to obtain detailed qualitative information about the center dynamics.
