Hölder continuity and laminarity of the Green currents for Hénon-like maps
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910076211560448 |
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| author | Bianchi, Fabrizio Dinh, Tien-Cuong Rakhimov, Karim |
| author_facet | Bianchi, Fabrizio Dinh, Tien-Cuong Rakhimov, Karim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01984 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hölder continuity and laminarity of the Green currents for Hénon-like maps Bianchi, Fabrizio Dinh, Tien-Cuong Rakhimov, Karim Complex Variables Dynamical Systems 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. |
| title | Hölder continuity and laminarity of the Green currents for Hénon-like maps |
| topic | Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/2407.01984 |