Infinitely Badly Approximable Affine Forms
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DOI: 10.1093/imrn/rnaf304
Abstract: A pair $(A,\textbf{b})$ of a real $m\times n$ matrix $A$ and $\textbf{b}\in \mathbb{R}^{m}$ is said to be infinitely badly approximable if $$ \begin{align*} & \liminf_{\textbf{q}\in\mathbb{Z}^{n}, \|\textbf{q}\|\to\infty} \|\textbf{q}\|^{\frac{n}{m}}\|A\textbf{q}-\textbf{b}\|_{\mathbb{Z}} =\infty, \end{align*} $$where $\|\cdot \|_{\mathbb{Z}}$ denotes the distance… read more here.
Keywords: textbf mathbb; badly approximable; textbf; approximable affine ... See more keywords
METRIC AND DIMENSIONAL PROPERTIES OF THE BADLY APPROXIMABLE SET FOR BETA-TRANSFORMATIONS
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DOI: 10.1142/s0218348x19500257
Abstract: For any [Formula: see text], let [Formula: see text] be the [Formula: see text]-transformation dynamical system. For any sequence [Formula: see text], we investigate the following badly approximable set: [Formula: see text] In this paper,… read more here.
Keywords: metric dimensional; see text; badly approximable; formula see ... See more keywords
BADLY APPROXIMABLE AND NONRECURRENT SETS FOR EXPANDING MARKOV MAPS
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DOI: 10.1142/s0218348x2150170x
Abstract: We consider the asymptotic behaviors of the orbits of an expanding Markov system [Formula: see text], and prove that the badly approximable set [Formula: see text] is of full Hausdorff dimension for any given sequence… read more here.
Keywords: see text; expanding markov; badly approximable; formula see ... See more keywords