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Remarks on the Dynamic of the Ruelle Operator and invariant differentials

P. M. Makienko<sup>ab

a</sup> Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
^b Instituto de Matematicas, UNAM at Cuernavaca Av. de Universidad s/N.

Abstract: 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.

Key words: Ruelle Operator, Julia set, quasiconformal deformation.

UDC: 517.95

MSC: Primary 37F45; Secondary 37F30

Received: 01.11.2008

Language: English