论文标题
单位球上的双曲线平衡和可逆零是可计算的
The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable
论文作者
论文摘要
在本说明中，我们构建了一种算法，该算法在输入结构稳定的平面动力流$ f $时，在封闭的单位磁盘上定义了，以任意准确性输出（双曲线）平衡点及其位置的确切数量。通过任意准确性，这意味着可以实现输入所需的任何准确性。该算法可以进一步扩展到一个求根算法，该算法计算确切的零数量，以及在$ \ mathbb {r}^{r}^{d} $的封闭单位球上定义的连续可区分函数$ f $的位置，但前提是$ f $的jacobian of $ f $ a $ f $ able $ f $ a $ f $ $ f $ f $ f $ f $ f $。此外，计算在$ f $中是统一的。
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 $f$.
