NORMAL FORMS FOR RETARDED FUNCTIONAL-DIFFERENTIAL EQUATIONS AND APPLICATIONS TO BOGDANOV-TAKENS SINGULARITY
NORMAL FORMS FOR RETARDED FUNCTIONAL-DIFFERENTIAL EQUATIONS AND APPLICATIONS TO BOGDANOV-TAKENS SINGULARITY
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DOI：
10.1006/jdeq.1995.1145
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发表时间：
1995-11-01
影响因子：
2.4
通讯作者：
MAGALHAES, LT
中科院分区：
文献类型：
--
作者：
FARIA, T;MAGALHAES, LT
该论文针对延迟泛函微分方程 (FDE)，讨论了与奇点处线性方程的无穷小生成器的不变空间相切的有限维不变流形上的流相关的范式计算。引入了适合计算这些范式的相空间，并导出了计算范式的充分非共振条件。作为一种应用，在一般情况和 x(t) = f(x-(t), x(t-1)) 形式的微分时滞方程的情况下，考虑了 Bogdanov-Takens 奇点的一般情况及其二阶非简并标量延迟 FDE 的通用展开。 (C) 1995 学术出版社
The paper addresses, for retarded functional differential equations (FDEs), the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity. A phase space appropriate to the computation of these normal forms is introduced, and adequate nonresonance conditions for the computation of the normal forms are derived. As an application, the general situation of Bogdanov-Takens singularity and its versal unfolding for scalar retarded FDEs with nondegeneracy at second order is considered, both in the general case and in the case of differential-delay equations of the form x(t) = f(x-(t), x(t-1)). (C) 1995 Academic Press, Inc.