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arXiv · 2309.07323

Dominated splitting from constant periodic data and global rigidity of Anosov automorphisms

Jonathan DeWitt·Andrey Gogolev
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Abstract

We show that a $\mathrm{GL}(d,\mathbb{R})$ cocycle over a hyperbolic system with constant periodic data has a dominated splitting whenever the periodic data indicates it should. This implies global periodic data rigidity of generic Anosov automorphisms of $\mathbb{T}^d$. Further, our approach also works when the periodic data is narrow, that is, sufficiently close to constant. We can show global periodic data rigidity for certain non-linear Anosov diffeomorphisms in a neighborhood of an irreducible Anosov automorphism with simple spectrum.

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Jonathan DeWitt, Andrey Gogolev. 2023-09-13. Dominated splitting from constant periodic data and global rigidity of Anosov automorphisms. https://arxiv.org/abs/2309.07323

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