Communications in Mathematical Physics

, Volume 129, Issue 3, pp 621–629 | Cite as

A dynamical system with integer information dimension and fractal correlation exponent

  • C. D. Cutler


In this paper we construct a family {Tγ}, 0<γ<1/2, of exact endomorphisms of [0, 1] such that the invariant measuremγ ofTγ is equivalent to Lebesgue measure but has fractal correlation exponent ν=2γ. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.


Neural Network Dynamical System Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • C. D. Cutler
    • 1
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

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