几乎处处线性化为Hurwitz的向量场
Vector fields whose linearisation is Hurwitz almost everywhere
摘要：
一个实矩阵是Hurwitz矩阵，如果它的特征值有负实部。二维全局渐近稳定性问题（BGAS）的推广如下：设$X:R^2-->R^2$是一个C^1向量场，其导数DX（p）对$R^2$中几乎所有p都是Hurwitz。则X的奇点集Sing（X）是空集、单点集或非离散集。此外，如果Sing（X）包含双曲奇点，则X拓扑等价于径向向量场$(x,y)--> (-x,-y)$。这将BGAS推广到向量场不一定是局部单同态的情况。
英文摘要：
A real matrix is Hurwitz if its eigenvalues have negative real parts. The following generalisation of the Bidimensional Global Asymptotic Stability Problem (BGAS) is provided: Let $X:R^2-->R^2$ be a C^1 vector field whose derivative DX(p) is Hurwitz for almost all p in $R^2$. Then the singularity set of X, Sing(X), is either an emptyset, a one--point set or a non-discrete set. Moreover, if Sing(X) contains a hyperbolic singularity then X is topologically equivalent to the radial vector field $(x,y)--> (-x,-y)$. This generalises BGAS to the case in which the vector field is not necessarily a local diffeomorphism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
