Geodesic
The Capacity of the Rational Preimage of a Compact Set
Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 790-799

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It is shown that a well-known expression for the capacity of the preimage of a compact set under a polynomial map remains valid in the case of a rational map, provided that the standard capacity of the preimage is replaced by its capacity in the external field determined by the poles in $\mathbb C$ of the rational function determining the map.
Keywords: capacity, transfinite diameter, rational map, symmetric compact set. 
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     author = {V. I. Buslaev},
     title = {The {Capacity} of the {Rational} {Preimage} of a {Compact} {Set}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a1/}
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V. I. Buslaev. The Capacity of the Rational Preimage of a Compact Set. Matematičeskie zametki, Tome 100 (2016) no. 6, pp. 790-799. http://geodesic.mathdoc.fr/item/MZM_2016_100_6_a1/