Hierarchy of chaotic maps with an invariant measure and their compositions

Details Hierarchy of chaotic maps with an invariant measure and their compositions Hierarchy of chaotic maps with an invariant measure and their compositions

2002-10-18

arxiv.org/abs/nlin/0210043v1

J. Nonlinear Math. Phys. 9, no. 1 (2002) 26-41

Nonlinear Sciences

Chaotic Dynamics

arxiv version is already official

Scientific paper

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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