dynamical systems and (perhaps) algebraic geometry

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Article #58

#58

From: Pascal Koiran
Date: Tue, 08 Sep 1992 11:07

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Hello,

Can someone provide a solution to the following problem, or give references
to related work in the litterature ?

Let f:[0,1]^n-->[0,1]^n (n>1) be a function of the form
f(x)=(P_1(x),P_2(x),...,P_n(x)) where the P_i's are polynomials.
Let's consider the iterates of f. Is the following situation possible ?

for all k, there exists an infinite number of k-cycles (by k-cycle, I mean
a cycle of length exactly k).

Generalize to rational functions instead of polynomials, and to analytic 
functions.

Thanks,

Pascal.

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From: koiran@ens.ens-lyon.fr (Pascal Koiran)
Subject: dynamical systems and (perhaps) algebraic geometry
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Date: Tue, 8 Sep 1992 11:07:54 GMT
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