In earlier work we defined a computational saddle transition problem which arises in the dynamics of certain hyperbolic toral automorphisms, and proved, using the shadowing lemma, that in an appropriate model of computation this problem is in Oracle $\mathbf{NP}$, up to a highly restricted oracle. In this note we show similar methods can be extended to a far larger class of dynamical systems, a class which is dense in the $C^0$-topology on Diff${}^1\left({\mathbf{T}}^{\mathbf{2}}\right)$. We adapt the fitted diffeomorphisms of Shub and Sullivan on the 2-Torus to a computational framework. Just as in their case, the resulting “well-fitted” toral automorphisms are structurally stable, and $C^0$-dense, and we show the associated saddle transition problems are, in our model, in Oracle $\mathbf{NP}$.

在较早的工作中，我们定义了一个计算鞍过渡问题，该问题在某些双曲线环自同构的动力学中出现，并使用遮蔽引理证明，该问题在适当的计算模型中存在于Oracle中 $\mathbf{NP}$，直到高度严格的预言。在本说明中，我们显示了类似的方法可以扩展到更大的一类动力学系统中，该类在系统中是密集的。$C^0$-Diff上的拓扑${}^{\mathrm{1个}}（{\mathbf{Ť}}^{\mathbf{2个}}）$。我们将2-Torus上的Shub和Sullivan拟合的拟同构调整为计算框架。就像在这种情况下一样，所产生的“拟合良好”的圆同构在结构上是稳定的，并且$C^0$-dense，并且在模型中我们证明了相关的鞍形过渡问题在Oracle中 $\mathbf{NP}$。