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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
Article

Abstract

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.

Keywords

Neural Network Dynamical System Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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