A generalization of Zeeman’s family
Sierakowski, Michał
Fundamenta Mathematicae, Tome 159 (1999), p. 277-286 / Harvested from The Polish Digital Mathematics Library
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E. C. Zeeman [2] described the behaviour of the iterates of the difference equation xn+1=R(xn,xn-1,...,xn-k)/Q(xn,xn-1,...,xn-k), n ≥ k, R,Q polynomials in the case k=1,Q=xn-1 and R=xn+α, x1,x2 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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:212424 
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     title = {A generalization of Zeeman's family},
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     volume = {159},
     year = {1999},
     pages = {277-286},
     zbl = {0947.39001},
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Sierakowski, Michał. A generalization of Zeeman’s family. Fundamenta Mathematicae, Tome 159 (1999) pp. 277-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv162i3p277bwm/

[00000] [1] F. Beukers and R. Cushman, Zeeman's monotonicity conjecture, J. Differential Equations 143 (1998), 191-200. | Zbl 0944.37026

[00001] [2] E. C. Zeeman, A geometric unfolding of a difference equation, J. Difference Equations Appl., to appear.

[00002] [3] E. C. Zeeman, Higher dimensional unfoldings of difference equations, lecture notes, ICTP Conference, Trieste, September 1998.