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A strong hot spot theorem |
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| Authors: | David H. Bailey Michal Misiurewicz |
| Affiliation: | Lawrence Berkeley Laboratory, 1 Cyclotron Road, Berkeley, California 94720 ; Department of Mathematical Sciences, Indiana University--Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, Indiana 46202-3216 |
| Abstract: | A real number  is said to be  -normal if every  -long string of digits appears in the base- expansion of  with limiting frequency  . We prove that  is  -normal if and only if it possesses no base- ``hot spot'. In other words,  is  -normal if and only if there is no real number  such that smaller and smaller neighborhoods of  are visited by the successive shifts of the base- expansion of  with larger and larger frequencies, relative to the lengths of these neighborhoods. |
| Keywords: | Normal numbers |
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