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On the convergence on nonlinear Padé--Chebyshev approximations to the multivalued analytic functions, variation of equilibrium energy and $S$-property of stationary compacts

Some new results on the convergence of nonlinear diagonal Padé--Chebyshev approximations to multivalued analytic function given on the segment $[-1,1]$, are proved. We show that these approximations converge to the given function in the "maxmimal" domain of its meromorphity and that the boundary of this maxmimal domain is an $S$-curve. The results of the work have been announced in abs/1009.4813 Bibliography: 57 items.