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arXiv nlin/0208024nlin.CD
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cn型和sn型椭圆混沌映射的单参数和多参数族

Hierarchy of one and many-parameter families of elliptic chaotic maps of cn and sn types

M. A. Jafarizadeh, S. Behnia

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14 pages, Latex
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摘要：

给出了区间[0，1]上cn型和sn型椭圆混沌映射的单参数和多参数族.证明了当椭圆函数参数k较小时，这些映射与文献[1，2]中的映射拓扑共轭，由此得到了这些映射在小k时的不变测度，并由此证明了这些映射具有与文献[1，2]中的映射相同的Kolmogorov-Sinai熵或等价的Lyapunov特征指数。当该参数消失时，映射被简化为上述参考文献中提出的映射。与通常的单参数映射族（如Logistic映射和Tent映射）相反，这些映射不表现出倍周期或周期n倍级联向混沌的过渡，但在某些参数值处具有单不动点吸引子，在这些参数值处它们直接分叉到混沌，而不恰好在这些参数值处具有周期n倍情形，这些参数值的李雅普诺夫特征指数开始为正。

英文摘要：

We present 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 [1,2], where using this we have been able to obtain the invariant measure of these maps for small k and thereof it is shown that these maps have the same Kolmogorov-Sinai entropy or equivalently Lyapunov characteristic exponent of the maps of references [1,2]}. As this parameter vanishes, the maps are reduced to the maps presented in above-mentioned reference. Also in 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 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 parameters whose Lyapunov characteristic exponent begin to be positive.

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