Far Eastern Mathematical Journal

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Remarks on the Dynamic of the Ruelle Operator and invariant differentials

P. M. Makienko

2008, issue 2, P. 180–205

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.

Ruelle Operator, Julia set, quasiconformal deformation

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