Symbolical and Geometrical Characterizations of Kronecker Sequences by Using the Accelerated Brun Algorithm
Vol. 7 (2000), No. 2, Page 163--193.
Fujita, Takahiko ; Ito, Shunji ; Ninomiya, Syoiti
Symbolical and Geometrical Characterizations of Kronecker Sequences by Using the Accelerated Brun Algorithm
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Abstract:
We give a \hbox{van der Corput}-type expression of the multi-dimensional \hbox{Kronecker} sequence and a geometrical characterization of its distribution property. We can consider the latter to be a multi-dimensional analogue of the "three-distance theorem." All these results were obtained by using the accelerated Brun algorithm.
Keywords: ergodic theory, irrational rotation, Kronecker sequence, low-discrepancy sequence, accelerated Brun algorithm, three-distance theorem
Mathematics Subject Classification (1991): 11A55, 11A63, 11K50
Mathematical Reviews Number: MR1768463
Received: 1998-10-12
