Geodesic
A generalization of Zeeman’s family
Fundamenta Mathematicae, Tome 162 (1999) no. 3, pp. 277-286.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

E. C. Zeeman [2] described the behaviour of the iterates of the difference equation $x_{n+1} = R(x_n,x_{n-1},...,x_{n-k})/Q(x_n,x_{n-1},..., x_{n-k})$, n ≥ k, R,Q polynomials in the case $k = 1, Q = x_{n-1}$ and $R = x_n+α$, $x_1,x_2$ positive, α nonnegative. We generalize his results as well as those of Beukers and Cushman on the existence of an invariant measure in the case when R,Q are affine and k = 1. We prove that the totally invariant set remains residual when the coefficients vary.
DOI : 10.4064/fm-162-3-277-286

Michał Sierakowski 1

1 
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Michał Sierakowski. A generalization of Zeeman’s family. Fundamenta Mathematicae, Tome 162 (1999) no. 3, pp. 277-286. doi : 10.4064/fm-162-3-277-286. http://geodesic.mathdoc.fr/articles/10.4064/fm-162-3-277-286/

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