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| Paper IPM / Physic / 6936 |
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| Abstract: | |||||
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We present a hierarchy of one- and many-parameter families of elliptic chaotic maps of cn and sn types at the interval [0,1]. It is proved that for small values of k the parameter of the elliptic function, these maps are topologically conjugate to the maps of references [J. Stat. Phys. 104 (2001); J. Nonlinear Phys. 9 (2002)]. Using this we have been able to obtain the invariant measure of these maps for small k and hence show that these maps have the same KolmogorovSinai entropy or (equivalently) Lyapunov characteristic exponent of the maps [J. Stat. Phys. 104 (2001); J. Nonlinear Phys. 9 (2002)]. Also, contrary to the usual family of one-parameter maps, such as the logistic and tent maps, these maps do not display period doubling or period-n-tupling cascade transition to chaos, but 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 parameters whose Lyapunov characteristic exponent begin to be positive.
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