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Hierarchy of chaotic maps with an invariant measure and their compositions

M. A. Jafarizadeh·S. Behnia
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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.

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M. A. Jafarizadeh, S. Behnia. 2002-10-18. Hierarchy of chaotic maps with an invariant measure and their compositions. https://doi.org/10.2991/jnmp.2002.9.1.4

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