Invariant currents and dynamical Lelong numbers |
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Authors: | Email author" target="_blank">Dan?ComanEmail author Vincent?Guedj |
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Institution: | (1) Department of Mathematics, Syracuse University, 13244-1150 Syracuse, NY;(2) Laboratoire Emile Picard, UMR 5580, Université Paul Sabatier, 31062 Toulouse Cédex 04, France |
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Abstract: | Let ƒ be a polynomial automorphism of ℂk of degree λ, 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 λ−n(ƒn)*S converges in the sense of currents on ℙk to a linear combination of the Green current T+ of ƒ 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 ƒ−1. |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 32H50 32U25 32U40 |
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