Communications in Mathematical Physics

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

Hausdorff dimension of order preserving sets

  • J. J. P. Veerman


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.


Neural Network Statistical Physic Complex System Periodic Orbit Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

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

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