论文标题
在间隔上进行分段连续地图的强大和通用属性
Robust and generic properties for piecewise continuous maps on the interval
论文作者
论文摘要
我们在紧凑间隔定义的分段$ \ Mathcal c^r $地图的集合中构建了适当的度量。尽管事实证明这一指标空间并不完整，但我们表明它确实是贝尔空间。作为应用程序，我们证明了这类系统的非分类临界点的鲁棒性，并显示了允许不变的鲍勒概率度量的分段Lipschitz地图的通用性。
We construct an appropriate metric on the collection of piecewise $\mathcal C^r$ maps defined on a compact interval. Although this metric space turns out to be not complete, we show that it is indeed a Baire space. As an application, we prove the robustness of non-degenerate critical points for this class of systems and we show the genericity of piecewise Lipschitz maps that admit an invariant Borel probability measure.
