Let f be a polynomial automorphism of Ck of degree lamda, whose rational extension to Pk maps the hyperplane at infinity to a single point. Given any positive closed current S on Pk of bidegree (1,1), we show that the sequence lamda−n(fn)*S converges in the sense of currents on Pk to a linear combination of the Green current T+ of f and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms of generalized Lelong numbers with respect to an invariant dynamical current for f−1.
Coman, Dan and Guedj, Vincent, "Invariant Currents and Dynamical Lelong Numbers" (2004). Mathematics Faculty Scholarship. 13.
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