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- W2955147563 abstract "In this paper, we study the weighted $n$-dimensional badly approximable points on manifolds. Given a $C^n$ differentiable non-degenerate submanifold $mathcal{U} subset mathbb{R}^n$, we will show that any countable intersection of the sets of the weighted badly approximable points on $mathcal{U}$ has full Hausdorff dimension. This strengthens a result of Beresnevich by removing the condition on weights and weakening the smoothness condition on manifolds. Compared to the work of Beresnevich, our approach relies on homogeneous dynamics. It turns out that in order to solve this problem, it is crucial to study the distribution of long pieces of unipotent orbits in homogeneous spaces. The proof relies on the linearization technique and representations of $mathrm{SL}(n+1,mathbb{R})$." @default.
- W2955147563 created "2019-07-12" @default.
- W2955147563 creator A5050967444 @default.
- W2955147563 date "2017-03-09" @default.
- W2955147563 modified "2023-09-26" @default.
- W2955147563 title "Badly approximable points on manifolds and unipotent orbits in homogeneous spaces" @default.
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- W2955147563 doi "https://doi.org/10.48550/arxiv.1703.03461" @default.
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