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- W2186815281 abstract "In this paper we show that the Hausdor dimension of the set of singular pairs is 4 . We also show that the action of diag(e t ;e t ;e 2t ) on SL3R=SL3Z admits divergent trajectories that exit to innity at arbitrarily slow prescribed rates, answering a question of A. N. Starkov. As a by-product of the analysis, we obtain a higher-dimensional generalization of the basic inequalities satised by convergents of continued fractions. As an illustration of the technique used to compute Hausdor dimension, we reprove a result of I. J. Good asserting that the Hausdor dimension of the set of real numbers with divergent partial quotients is 1 ." @default.
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- W2186815281 date "2011-01-01" @default.
- W2186815281 modified "2023-09-27" @default.
- W2186815281 title "dimension of the set of singular pairs" @default.
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