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Paper   IPM / Physic / 6848
School of Physics
  Title:   Hierarchy of Chaotic Maps with An Invariant Measure
1.  M.A. Jafarizadeh
2.  S. Behnia
3.  S. Khorram
4.  H. Nagshara
  Status:   Published
  Journal: J. Stat. Phys.
  Vol.:  104
  Year:  2001
  Pages:   1013-1028
  Supported by:  IPM
We give hierarchy of one-parameter family ϕ(α,x) of maps at the interval [0,1] with an invariant measure. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent of these maps analytically, where the results thus obtained have been approved with the numerical simulation. In contrary to the usual one-parameter family of maps such as logistic and tent maps, these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor for certain values of the parameter, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at those values of the parameter whose Lyapunov characteristic exponent begins to be positive.

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