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- W4320823210 abstract "As a model to provide a hands-on, elementary understanding of chaotic dynamics in dimension three, we introduce a $C^2$-open set of diffeomorphisms of $mathbb R^3$ having two horseshoes with different dimensions of instability. We prove that: the unstable set of one horseshoe and the stable set of the other are of Hausdorff dimension nearly $2$ whose cross sections are Cantor sets; the intersection of the unstable and stable sets contains a fractal set of Hausdorff dimension nearly $1$. As a corollary we detect $C^2$-robust heterodimensional cycles. Our proof employs the theory of normally hyperbolic invariant manifolds and the thicknesses of Cantor sets." @default.
- W4320823210 created "2023-02-15" @default.
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- W4320823210 date "2020-11-24" @default.
- W4320823210 modified "2023-09-29" @default.
- W4320823210 title "Hausdorff dimension of Cantor intersections and robust heterodimensional cycles for heterochaos horseshoe maps" @default.
- W4320823210 doi "https://doi.org/10.48550/arxiv.2011.12264" @default.
- W4320823210 hasPublicationYear "2020" @default.
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