Geodesic
Variation of the equilibrium energy and the $S$-property of stationary compact sets
Sbornik. Mathematics, Tome 202 (2011) no. 12, pp. 1831-1852

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This paper studies a variation of the equilibrium energy for a certain fairly general functional which appears naturally in the solution of many rational approximation problems of multi-valued analytic functions. The main result of this work states that for the energy functional under consideration and a certain class of admissible compact sets, related to the function to be approximated, the corresponding stationary compact set is fully characterized by the so-called $S$-property. Bibliography: 38 titles.
Keywords: rational approximation, equilibrium distributions, stationary compact set, $S$-property.
Mots-clés : orthogonal polynomials, Padé approximants 
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A. Martínez-Finkelshtein; E. A. Rakhmanov; S. P. Suetin. Variation of the equilibrium energy and the $S$-property of stationary compact sets. Sbornik. Mathematics, Tome 202 (2011) no. 12, pp. 1831-1852. http://geodesic.mathdoc.fr/item/SM_2011_202_12_a4/