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Dynamics of polynomial mappings of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 124, Number 1, February 2002
- pp. 75-106
- 10.1353/ajm.2002.0002
- Article
- Additional Information
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We study the dynamics of polynomial self mappings f of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]. We construct, for a large class of mappings, an invariant measure μ which is mixing and of maximal entropy hμ(f) = max (log dt(f), log λ1(f)), where dt(f) is the topological degree of f and λ1(f) its first dynamical degree. To achieve this, we look at the meromorphic extensions of f to smooth minimal compactifications of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] When a good compactification is found, we construct an f*-invariant Green current T which contains many dynamical informations. When δ := dt(f)/λ1(f) > 1, the measure μ is obtained as μ = ddc(υT), where υ is a partial Green function defined on the support of T. When δ < 1, μ = T ∧ T- where T- is a globally defined f*-invariant current.