### Abstract

Let f be a polynomial automorphism of ℂ ^{k} of degree λ, whose rational extension to ℙ ^{k} maps the hyperplane at infinity to a single point. Given any positive closed current S on ℙ ^{k} of bidegree (1,1), we show that the sequence λ ^{-n}(f ^{n})*S converges in the sense of currents on ℙ ^{k} 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}.

Original language | English (US) |
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Pages (from-to) | 199-213 |

Number of pages | 15 |

Journal | Journal of Geometric Analysis |

Volume | 14 |

Issue number | 2 |

DOIs | |

State | Published - 2004 |

### Keywords

- Dynamics of polynomial automorphisms
- Lelong numbers
- currents

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Coman, D., & Guedj, V. (2004). Invariant currents and dynamical Lelong numbers.

*Journal of Geometric Analysis*,*14*(2), 199-213. https://doi.org/10.1007/BF02922068