Local complexity functions of interval exchange transformations |
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| Authors: | V Afraimovich R Rechtman |
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| Institution: | 1. Harvard School of Public Health, 677 Huntington Avenue, Boston, MA 02115, USA;2. Department of Economics, University of Vermont, 237 Old Mill, Burlington, VT, USA |
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| Abstract: | We studied numerically complexity functions for interval exchange transformations. We have shown that they grow linearly in time as well as the ?-complexity function. Moreover, we found out that they depend also linearly on ? where ? is the Lebesgue measure of a set of initial points. This allows us to hypothesize that the dimension of the measure related to the ?-complexity function could be determined by studying the dependence of local complexity functions on ?. |
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