On an application of convexity to discrete systems. (English) Zbl 0588.93048

Poljak, Svatopluk; Turzík, Daniel

Discrete Appl. Math. 13, 27-32 (1986).

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

Keywords:

convexity, discrete systems

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