K-divergent lattices
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913472597458944 |
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| author | Lachman, Guy Rao, Anurag Shapira, Uri Yifrach, Yuval |
| author_facet | Lachman, Guy Rao, Anurag Shapira, Uri Yifrach, Yuval |
| contents | We introduce a novel concept in topological dynamics, referred to as $k$-divergence, which extends the notion of divergent orbits. Motivated by questions in the theory of inhomogeneous Diophantine approximations, we investigate this notion in the dynamical system given by a certain flow on the space of unimodular lattices in $\mathbb{R}^d$. Our main result is the existence of $k$-divergent lattices for any $k\geq 0$. In fact, we utilize the emerging theory of parametric geometry of numbers and calculate the Hausdorff dimension of the set of $k$-divergent lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | K-divergent lattices Lachman, Guy Rao, Anurag Shapira, Uri Yifrach, Yuval Dynamical Systems We introduce a novel concept in topological dynamics, referred to as $k$-divergence, which extends the notion of divergent orbits. Motivated by questions in the theory of inhomogeneous Diophantine approximations, we investigate this notion in the dynamical system given by a certain flow on the space of unimodular lattices in $\mathbb{R}^d$. Our main result is the existence of $k$-divergent lattices for any $k\geq 0$. In fact, we utilize the emerging theory of parametric geometry of numbers and calculate the Hausdorff dimension of the set of $k$-divergent lattices. |
| title | K-divergent lattices |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2307.09054 |