On the Regularity of Invariant Foliations

    2024, Volume 29, Number 1, pp.  6-24

    Author(s): Turaev D. V.

    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

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