Brolin's theorem for curves in two complex dimensions

Charles Favre; Mattias Jonsson

doi:10.5802/aif.1985

Brolin's theorem for curves in two complex dimensions

Charles Favre
, Mattias Jonsson

Research output: Contribution to journal › Article › peer-review

Abstract

Given a holomorphic mapping f : ℙ² → ℙ ² of degree d ≥ 2 we give sufficient conditions on a positive closed (1,1) current of S of unit mass under which d^-n f ⁿ* S converges to the Green current as n → ∞. We also conjecture necessary conditions for the same convergence.

Original language	English
Pages (from-to)	1461-1501+x+vi
Journal	Annales de l'Institut Fourier
Volume	53
Issue number	5
DOIs	https://doi.org/10.5802/aif.1985
Publication status	Published - 1 Jan 2003
Externally published	Yes

Keywords

Asymptotic multiplicities
Currents
Equidistribution
Holomorphic dynamics
Kiselman numbers
Lelong numbers
Volume estimates

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10.5802/aif.1985

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title = "Brolin's theorem for curves in two complex dimensions",

abstract = "Given a holomorphic mapping f : ℙ2 → ℙ 2 of degree d ≥ 2 we give sufficient conditions on a positive closed (1,1) current of S of unit mass under which d-n f n* S converges to the Green current as n → ∞. We also conjecture necessary conditions for the same convergence.",

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author = "Charles Favre and Mattias Jonsson",

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AU - Jonsson, Mattias

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AB - Given a holomorphic mapping f : ℙ2 → ℙ 2 of degree d ≥ 2 we give sufficient conditions on a positive closed (1,1) current of S of unit mass under which d-n f n* S converges to the Green current as n → ∞. We also conjecture necessary conditions for the same convergence.

KW - Asymptotic multiplicities

KW - Currents

KW - Equidistribution

KW - Holomorphic dynamics

KW - Kiselman numbers

KW - Lelong numbers

KW - Volume estimates

U2 - 10.5802/aif.1985

DO - 10.5802/aif.1985

M3 - Article

AN - SCOPUS:1342326308

SN - 0373-0956

VL - 53

SP - 1461-1501+x+vi

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 5

ER -

Brolin's theorem for curves in two complex dimensions

Abstract

Keywords

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