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Communications in Mathematical Physics

, Volume 127, Issue 2, pp 313–317 | Cite as

Hausdorff dimension of order preserving sets

  • J. J. P. Veerman
Article

Abstract

Letg aC2 generic bimodal map of the circle. We prove that the closure of the union of the order preserving recurrent sets with irrational rotation number has Hausdorff dimension zero. This set contains order preserving periodic orbits with each rotation numberp/q in the rotation interval ofg.

Keywords

Neural Network Statistical Physic Complex System Periodic Orbit 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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References

  1. Falconer, K.J.: The geometry of fractal sets. Cambridge: Cambridge University Press 1985Google Scholar
  2. Veerman, J.J.P.: On resonance widths in dynamical systems. Thesis, Cornell University 1986Google Scholar
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  5. Smale, S.: Bull. Am. Math. Soc.73, 747–817 (1967)Google Scholar
  6. Swiatek, G.: Endpoints of rotation intervals for maps of the circle. Preprint Warsaw 1987Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • J. J. P. Veerman
    • 1
  1. 1.Rockefeller UniversityNew YorkUSA

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