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Paper   IPM / P / 6848
School of Physics
Title:   Hierarchy of Chaotic Maps with An Invariant Measure
Author(s):
 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
Abstract:
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.