Study of convergence in a~rectification problem

O. N. Stavskaya

Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 119-137

Résumé

The problem of “rectification” is considered of the plane motion of a polygonal line $\overline A(t)$ specified by its $n+1$ vertices. The motion is defined by an operator $\mathfrak A$ in $(2n+2)$-dimensional space whose infinite repetition must rectify the polygonal line. The rules of motion of the vertices are local and homogeneous for all the internal vertices of the polygonal line. The behavior of $\overline A(t)$ in the neighborhood of stationary points is studied, and global convergence to these points from certain initial states is proved for $t\to\infty$. Figures: 4. Bibliography: 2 titles.