A dynamical system with integer information dimension and fractal correlation exponent |
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| Authors: | C D Cutler |
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| Institution: | (1) Department of Statistics and Actuarial Science, University of Waterloo, N2L 3G1 Waterloo, Ontario, Canada |
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| Abstract: | In this paper we construct a family {T
 }, 0<<1/2, of exact endomorphisms of 0, 1] such that the invariant measurem
ofT
is equivalent to Lebesgue measure but has fractal correlation exponent  =2. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.Research supported by the Natural Sciences and Engineering Research Council of Canada |
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| Keywords: | |
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