We show that the stable invariant foliation of codimension 1 near a zero-dimensional hyperbolic set of a \(C^{\beta}\) map with \(\beta>1\) is \(C^{1+\varepsilon}\) with some \(\varepsilon>0\). The result is applied to the restriction of higher regularity maps to normally hyperbolic manifolds. An application to the theory of the Newhouse phenomenon is discussed.

中文翻译：

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论不变叶状结构的规律性

我们证明，在具有\( \beta>1 \) 的 \(C^{\beta}\)映射的零维双曲集附近，余维 1 的稳定不变叶化为\(C^{1+\varepsilon} \)与一些\(\varepsilon>0\)。结果应用于将更高正则性映射限制为正常双曲流形。讨论了纽豪斯现象理论的应用。