耗散哈密顿铅笔的等价类
On equivalence classes of dissipative Hamiltonian pencils
AI总结：
该研究在Pokrzywa严格等价轨道序框架下，刻画特定耗散哈密顿矩阵铅笔的等价类，分析轨道闭包性质，推导退化限制，得到奇异情况的Kronecker标准形部分结果并辅以示例说明。
AI中文摘要：
我们在Pokrzywa严格等价轨道的序框架下，研究形如$\boldsymbol{\textit{λE} - (J-R)Q}$的矩阵铅笔，其中满足$\boldsymbol{Q^*E = E^*Q \textbf{≥} 0}$、$\boldsymbol{J^* = -J}$、$\boldsymbol{R^* = R \textbf{≥} 0}$，且$\boldsymbol{\textit{λE} - Q}$正则。我们刻画了其极大元，分析了轨道闭包的若干性质，推导了当$\boldsymbol{Q = I}$时可能退化的限制。还考虑了$\boldsymbol{\textit{λE} - Q}$可能奇异的情况（该情况自然出现在轨道闭包研究中），得到了关于Kronecker标准形的部分结果，并用大量示例阐释了该理论。
英文摘要：
We study matrix pencils of the form $λE - (J-R)Q$, where $Q^*E = E^*Q \geq 0$, $J^* = -J$, $R^* = R \geq 0$, and $λE - Q$ is regular, in the framework of Pokrzywa's ordering of strict equivalence orbits. We characterise the maximal elements, analyse some properties of the orbit closures, and derive a restriction on possible degenerations when $Q = I$. We also consider the case where $λE - Q$ may be singular, which naturally arises in the study of orbit closures, and obtain a partial result on the Kronecker canonical form. The theory is illustrated by numerous examples.
