Geodesic
Remarks on the Dynamic of the Ruelle Operator and invariant differentials
Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 180-205.

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Let $R$ be a rational map. We are interesting in the dynamic of the Ruelle operator of $R$ on suitable spaces of differential forms. In particular the necessary and sufficient conditions (in terms of convergence of sequences of measures) of existence of invariant measurable conformal structures on $J(R)$ are obtained. 
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P. M. Makienko. Remarks on the Dynamic of the Ruelle Operator and invariant differentials. Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 180-205. http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a4/

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