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.
Keywords:
homoclinic tangency, thickness of Cantor set, invariant manifold
Citation:
Turaev D. V., On the Regularity of Invariant Foliations, Regular and Chaotic Dynamics,
2024, Volume 29, Number 1,
pp. 6-24