单位球上的双曲平衡集和可逆零点集是可计算的
The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable
摘要：
在本文中，我们构造了一个算法，在输入的结构稳定的平面动力流$f$定义在封闭的单位盘上的描述，输出的（双曲）平衡点和它们的位置与任意精度的确切数量。任意精度意味着可以实现输入所需的任何精度。该算法可以进一步扩展到一个寻根算法，计算精确的零点的数量以及每个零点的位置的连续可微函数$f$上定义的封闭单位球$\mathbb{R}^{d}$，提供的雅可比矩阵$f$是可逆的，在每个零点的$f$ ;此外，计算是均匀的$f$。
英文摘要：
In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations with arbitrary accuracy. By arbitrary accuracy it is meant that any accuracy required by the input can be achieved. The algorithm can be further extended to a root-finding algorithm that computes the exact number of zeros as well the location of each zero of a continuously differentiable function $f$ defined on the closed unit ball of $\mathbb{R}^{d}$, provided that the Jacobian of $f$ is invertible at each zero of $f$; moreover, the computation is uniform in $f$.
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。
