中文

Journal of Shanghai University（Natural Science Edition） ›› 2010, Vol. 16 ›› Issue (3): 242-247.doi: O175.12

• Mathematics.Physics and Chemistry • Previous Articles     Next Articles

Dynamical Properties of Two-Torus and Planar Piecewise Parabolic Maps

LIN Cong-ping,FU Xin-chu,WANG Kai-hua   

  1. (1. College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China; 
    2. College of Sciences, Shanghai University, Shanghai 200444, China)
  • Online:2010-06-28 Published:2010-06-28

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Abstract:

This paper discusses isomorphism between invertible torus parabolic maps and periodicity where periodic point sets in horocyclic case are dense in the torus topology, and some semi-rational cases possess periodic points of all periods. For the integral parabolic maps on the torus, the topological entropy is zero. Symbolic entropy and complexity of planar piecewise parabolic maps are investigated. Their difference under the plane topology and the torus topology respectively for the same torus parabolic maps is also discussed.

Key words: 2-torus parabolic map; planar piecewise parabolic map; periodicity; symbolic entropy; complexity