平衡点谱型的代数几何分类
An algebro-geometric classification of spectral types of equilibria
摘要：
我们给三个代数方程，允许一个给定的$m$维动力系统的平衡的所有光谱类型的几何分类，我们彻底分析他们在3维和4维。由这些方程定义的轨迹对应于一定类型的分叉。这种轨迹的补充给出了开放域中的不变量空间的几何分解，其中平衡具有给定的谱类型。这种方法的有用性在于，当处理参数依赖的动力系统时，轨迹从不变量空间拉回到参数空间给出了当前动力系统的参数空间的分叉分解。我们也给出了显式计算谱指数的有效方法。
英文摘要：
We give three algebraic equations which allow a geometric classification of all spectral types of equilibria of a given $m$-dimensional dynamical system, and we analyse them thoroughly in dimension 3 and 4. The loci defined by these equations correspond to definite types of bifurcations. The complement of such loci give a geometric decomposition of the space of invariants in open domains in which the equilibrium has a given spectral types. The usefulness of this approach lays in the fact that, when dealing with a parameter-dependent dynamical system, the pull-back of the loci from the space of invariants to the parameter space gives the bifurcation-decomposition of parameter space for the dynamical system at hand. We also give effective methods to explicitly compute the spectral indices.
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。
