AI 中文总结
研究四类含一或两个时滞的自治微分时滞方程平衡点附近周期和反对称解的分支，通过转化为哈密顿系统，利用哈密顿分支理论及马斯洛夫型指标计算，得到相关分支结果。
AI 中文摘要
我们研究了四类含一个或两个时滞势微分时滞方程平衡点附近周期和反对称解的分支。通过将每个系统重新表述为（广义）哈密顿系统，并应用作者近期发展的哈密顿分支理论，我们得到了法代尔 - 拉宾诺维茨和拉宾诺维茨型的分支结果。该分析依赖于相关线性哈密顿系统基本解的马斯洛夫型指标的计算。
英文摘要
We investigate bifurcations of periodic and antiperiodic solutions near equilibria for four classes of potential differential-delay equations involving one or two delays. By reformulating each system as a (generalized) Hamiltonian system, and applying the Hamiltonian bifurcation theory recently developed by the author we obtain bifurcation results of both Fadell--Rabinowitz and Rabinowitz type. The analysis relies on the computation of Maslov--type indices for fundamental solutions of the associated linear Hamiltonian systems.
CommentsLatex, 96 pages. Sufficient conditions under weaker assumptions have been added to the relevant theorems and corollaries, with corresponding adjustments made to their statements and proofs. Typos and a mistake in the proof of Theorem 6.3 have been corrected
