On a generalization of the logistic map

Details On a generalization of the logistic map On a generalization of the logistic map

2000-03-07

arxiv.org/abs/nlin/0003017v1

Nonlinear Sciences

Chaotic Dynamics

5 pages, 2 eps figures

Scientific paper

A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based on the construction of conjugacies. Moreover, it is shown that, despite the dissimilarity of their polynomial expressions, all the maps possess the same invariant density. Other algebraic properties of the family, which shows some relationship with the set of Tschebysheff polynomials, are also investigated.

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