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GEOMETRIC LORENZ ATTRACTOR AND ORBITAL SHADOWING PROPERTY

  • Sessary, Mohammad Reza Bagherzad (Department Mathematics, Cungnam National University) ;
  • Lee, Keonhee (Department of Mathematics, Cungnam National University)
  • Received : 2015.03.30
  • Published : 2016.03.31

Abstract

Komuro [3] proved that geometric Lorentz attractor does not satisfy the shadowing property. In this paper we study the condition under which geometric Lorenz attractor has the orbital shadowing property that is weaker than the shadowing property.

Keywords

geometric Lorenz model;strange attractor;orbital shadowing property

Acknowledgement

Supported by : National Research Foundation (NRF)

References

  1. V. Araujo and M. J. Pacifico, Three Dimensional Flow, Springer, 2010.
  2. J. Guckenheimer, A strange, strange attractor, The Hopf bifurcation theorem and its application, ed. by J. E Marsden and M.McCracken, Springer-Verlag 19 (1976), 368-381.
  3. M. Komuro, Lorenz attractors do not have the pseudo-orbit tracing property, J. Math. Soc. Japan 37 (1985), 489-514. https://doi.org/10.2969/jmsj/03730489
  4. R. F. Williams, Structure of Lorenz attractors, IHES Publ. Math. 50 (1979), 73-99. https://doi.org/10.1007/BF02684770