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Mat. Sb. (N.S.), 1974, Volume 94(136), Number 1(5), Pages 74–88 (Mi msb3633)  

Proof of convergence in the problem of rectification

G. A. Gal'perin


Abstract: The behavior of the vertices $A_1(t),…,A_n(t)$ of a polygonal line $\mathbf A(t)$ situated in $k$-dimensional Euclidean space is considered as $t\to\infty$ (each point $A_i(t\pm1)$, $1<i<n$, is a linear combination of the points $A_{i-1}(t)$, $A_i(t)$ and $A_{i+1}(t)$; the points $A_1(t+1)$ and $A_n(t+1)$ are linear combinations of $A_1(t)$ and $A_2(t)$, and $A_{n-1}(t)$ and $A_n(t)$, respectively). It is proved that for any initial position $\mathbf A(0)$ the polygonal lines $\mathbf A(t)$ converge to one of two possible limits, namely a stationary or quasistationary polygonal line.
Figures: 1.
Bibliography: 2 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 23:1, 69–83

Bibliographic databases:

UDC: 513.7
MSC: 50B30, 92A05
Received: 22.05.1973

Citation: G. A. Gal'perin, “Proof of convergence in the problem of rectification”, Mat. Sb. (N.S.), 94(136):1(5) (1974), 74–88; Math. USSR-Sb., 23:1 (1974), 69–83

Citation in format AMSBIB
\Bibitem{Gal74}
\by G.~A.~Gal'perin
\paper Proof of convergence in the problem of rectification
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 94(136)
\issue 1(5)
\pages 74--88
\mathnet{http://mi.mathnet.ru/msb3633}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=351497}
\zmath{https://zbmath.org/?q=an:0305.50004}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 23
\issue 1
\pages 69--83
\crossref{https://doi.org/10.1070/SM1974v023n01ABEH001714}


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