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Paper   IPM / P / 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.