Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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F. Bianchi - T. C. Dinh - K. Rakhimov

Hölder continuity and laminarity of the Green currents for Hénon-like maps

created by bianchi on 04 Jul 2024



Inserted: 4 jul 2024
Last Updated: 4 jul 2024

Year: 2024

ArXiv: 2407.01984 PDF


Under a natural assumption on the dynamical degrees, we prove that the Green currents associated to any H\'enon-like map in any dimension have H\"older continuous super-potentials, i.e., give H\"older continuous linear functionals on suitable spaces of forms and currents. As a consequence, the unique measure of maximal entropy is the Monge-Amp\`ere of a H\"older continuous plurisubharmonic function and has strictly positive Hausdorff dimension. Under the same assumptions, we also prove that the Green currents are woven. When they are of bidegree $(1,1)$, they are laminar. In particular, our results generalize results known until now only in algebraic settings, or in dimension 2.

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