Lengths of lemniscates. Variations of rational functions

The problem under consideration is the estimate of the length of the lemniscate where 0.$ SRC=http://ej.iop.org/images/1064-5616/198/8/A03/tex_sm_3875_img2.gif/> It is shown that . A sharp estimate for the variation of a rational function along a curve of bounded rotation of the secant is also obtained. Bibliography: 15 titles.

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