HÖLDER CONTINUITY AND LAMINARITY OF THE GREEN CURRENTS FOR HÉNON-LIKE MAPS
Abstract
Abstract Under a natural assumption on the dynamical degrees, we prove that the Green currents associated to any Hénon-like map in any dimension have Hölder continuous super-potentials, i.e., give Hölder continuous linear functionals on suitable spaces of forms and currents. As a consequence, the unique measure of maximal entropy is the Monge-Ampère of a Hölder 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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Navier-Stokes equation solutions
Publication details
- Journal / source
- Journal of the Institute of Mathematics of Jussieu
- Publisher
- Cambridge University Press (CUP)
- Volume
- 25
- Issue
- 2
- Pages
- 1363–1392
- Publication date
- 2 February 2026
- Language
- EN