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Paper   IPM / Physic / 6851
School of Physics
  Title:   Hierarchy of Chaotic maps with An Invariant Measure and Their Compositions
  Author(s): 
1.  M.A. Jafarizadeh
2.  S. Behnia
  Status:   Published
  Journal: J. Nonlinear Math. Phys.
  Vol.:  9
  Year:  2002
  Pages:   26-41
  Supported by:  IPM
  Abstract:
We give a hierarchy of many-parameter families of maps of the interval [0,1] with an invariant measure and using the measure, we calculate Kolmogorov-Sinai entropy of these maps analytically. In contrary to the usual one-dimensional maps these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain region of parameters space, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at certain values of the parameters.

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