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- From: koiran@ens.ens-lyon.fr (Pascal Koiran)
- Subject: Re: dynamical systems and (perhaps) algebrai
- References: <a_rubin.715980149@dn66>
- Message-ID: <BuDLsK.ELL@ens-lyon.fr>
- Sender: Daniel Grayson <dan@math.uiuc.edu>
- Reply-To: koiran@ens.ens-lyon.fr
- X-Submissions-To: sci-math-research@uiuc.edu
- Organization: Ecole Normale Superieure de Lyon
- X-Administrivia-To: sci-math-research-request@uiuc.edu
- Approved: Daniel Grayson <dan@math.uiuc.edu>
- Date: Thu, 10 Sep 1992 18:53:08 GMT
- Lines: 20
-
- The solution proposed by Arthur Rubin in sci.math.research is perfectly
- correct. However, I'd like to have a less degenerate exemple. One might
- perhaps add a condition like
-
- "all the variables x_1,...,x_n must occur in each P_i"
-
- or a similar but weaker condition like
-
- "The set of variables {1,...,n} cannot be partitioned in two subsets I1 and
- I2 such that the two subsystems (x_i)_{i in I1} and (x_i)_{i in I2} evolve
- independently from each other".
-
- The motivation behind my question is to find a dynamical property
- differentiating piecewise-linear functions from polynomial, rational, or
- analytic function on [0,1]^n. Any suggestion on this is welcome. For n=2,
- there exist non degenerate piecewise-linear functions with infinitely many
- k-cycles for every k (hence my question).
-
- Pascal.
-
-