The asymptotics of Hermite-Padé polynomials for two Markov-type functions

A problem is solved on the limit distribution of the zeros of polynomials which are simultaneously orthogonal on two intervals $\Delta_1$ and $\Delta_2$ of the real line such that $\Delta_1\subset\Delta_2$, under the assumption that the ratio of the weight functions on $\Delta_1$ is a Markov-type function generated by a third interval $\Delta_3$ not intersecting $\overset{\circ}\Delta_2$.
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