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| Paper IPM / P / 6848 |
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| Abstract: | |||||||||
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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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