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

Dinh, Tien-Cuong

Bull. Soc. Math. Fr. 133, No. 3, 363-394 (2005).

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

Keywords:

repelling points; equilibrium measure; polynomial correspondence; Lojasiewicz exponent; generic point; periodic points