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On an application of convexity to discrete systems. (English) Zbl 0588.93048
We prove the following result: Let A be a symmetric matrix, f be a gradient (or certain subgradient) of a convex function, and \(\{y_ i\}\) be a sequence defined by \(y_{i+1}=f(Ay_ i)\), \(y_ 0\) arbitrary. Then the only possible periods of \(\{y_ i\}\) are 1 or 2.

MSC:
93C55 Discrete-time control/observation systems
26B25 Convexity of real functions of several variables, generalizations
39A12 Discrete version of topics in analysis
34C25 Periodic solutions to ordinary differential equations
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