Hierarchy of Chaotic Maps with an Invariant Measure

Details Hierarchy of Chaotic Maps with an Invariant Measure Hierarchy of Chaotic Maps with an Invariant Measure

2000-03-14

arxiv.org/abs/nlin/0003036v1

Nonlinear Sciences

Chaotic Dynamics

18 pages (Latex), 7 figures

Scientific paper

10.1016/S0167-2789(01)00325-6

We give hierarchy of one-parameter family F(a,x) of maps of 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 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 at certain parameter values, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at these values of parameter whose Lyapunov characteristic exponent begins to be positive.

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