Equidistribution of expanding degenerate manifolds in the space of lattices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866912032105693184 |
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| author | Shah, Nimish A. Yang, Pengyu |
| author_facet | Shah, Nimish A. Yang, Pengyu |
| contents | For the space of unimodular lattices in a Euclidean space, we give necessary and sufficient conditions for equidistribution of expanding translates of any real-analytic submanifold under a diagonal flow. This extends the earlier result of Shah in the case of non-degenerate submanifolds.
We apply the above dynamical result to show that if the affine span of a real-analytic submanifold in a Euclidean space satisfies certain Diophantine and arithmetic conditions, then almost every point on the manifold is not Dirichlet-improvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13952 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Equidistribution of expanding degenerate manifolds in the space of lattices Shah, Nimish A. Yang, Pengyu Dynamical Systems Number Theory Primary 37A17, 11J83, Secondary 22E46, 14L24, 11J13 For the space of unimodular lattices in a Euclidean space, we give necessary and sufficient conditions for equidistribution of expanding translates of any real-analytic submanifold under a diagonal flow. This extends the earlier result of Shah in the case of non-degenerate submanifolds. We apply the above dynamical result to show that if the affine span of a real-analytic submanifold in a Euclidean space satisfies certain Diophantine and arithmetic conditions, then almost every point on the manifold is not Dirichlet-improvable. |
| title | Equidistribution of expanding degenerate manifolds in the space of lattices |
| topic | Dynamical Systems Number Theory Primary 37A17, 11J83, Secondary 22E46, 14L24, 11J13 |
| url | https://arxiv.org/abs/2112.13952 |