Hierarchy of piecewise non-linear maps with non-ergodicity behavior

Details Hierarchy of piecewise non-linear maps with non-ergodicity behavior Hierarchy of piecewise non-linear maps with non-ergodicity behavior

2004-09-26

arxiv.org/abs/nlin/0409054v1

J.Phys.A:Math.Gen. 37 (2004) 9403-9417

Nonlinear Sciences

Chaotic Dynamics

18 pages, 8 figures

Scientific paper

10.1088/0305-4470/37/40/006

We study the dynamics of hierarchy of piecewise maps generated by one-parameter families of trigonometric chaotic maps and one-parameter families of elliptic chaotic maps of $\mathbf{cn}$ and $\mathbf{sn}$ types, in detail. We calculate the Lyapunov exponent and Kolmogorov-Sinai entropy of the these maps with respect to control parameter. Non-ergodicity of these piecewise maps is proven analytically and investigated numerically . The invariant measure of these maps which are not equal to one or zero, appears to be characteristic of non-ergodicity behavior. A quantity of interest is the Kolmogorov-Sinai entropy, where for these maps are smaller than the sum of positive Lyapunov exponents and it confirms the non-ergodicity of the maps.

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