## Distribution des préimages et des points périodiques d’une correspondance polynomiale. (Distribution of preimages and periodic points of a polynomial correspondence.)(French. English summary)Zbl 1090.37032

Summary: We construct an equilibrium measure $$\mu$$ for a polynomial correspondence $$F$$ of Lojasiewicz exponent $$\ell>1$$. We then show that $$\mu$$ can be built as the distribution of preimages of a generic point and that the repelling periodic points are equidistributed on the support of $$\mu$$. Using these results, we give a characterization of infinite uniqueness sets for polynomials.

### MSC:

 37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets 32H30 Value distribution theory in higher dimensions 32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
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