Dimension of equilibrium measures for complex maps
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911850179854336 |
|---|---|
| author | Ovadia, Snir Ben He, Yan Mary |
| author_facet | Ovadia, Snir Ben He, Yan Mary |
| contents | For certain families of complex maps, we give a formula for the Hausdorff dimension of the equilibrium measure. In particular, given an endomorphism $f$ of $\mathbb C\mathbb P^k$ of algebraic degree $d \ge2$, and given the equilibrium measure $μ$ with Lyapunov exponents $χ_1\geq \ldots\geq χ_k$, we show $\dim_\mathrm{H}(μ) = \log d\sum_{i\leq k}\frac{1}{χ_i}$ where $\dim_\mathrm{H}(μ)$ is the Hausdorff dimension of the measure $μ$. This gives an answer to the question of Fornæss and Sibony, and proves the Binder-DeMarco Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension of equilibrium measures for complex maps Ovadia, Snir Ben He, Yan Mary Dynamical Systems Complex Variables For certain families of complex maps, we give a formula for the Hausdorff dimension of the equilibrium measure. In particular, given an endomorphism $f$ of $\mathbb C\mathbb P^k$ of algebraic degree $d \ge2$, and given the equilibrium measure $μ$ with Lyapunov exponents $χ_1\geq \ldots\geq χ_k$, we show $\dim_\mathrm{H}(μ) = \log d\sum_{i\leq k}\frac{1}{χ_i}$ where $\dim_\mathrm{H}(μ)$ is the Hausdorff dimension of the measure $μ$. This gives an answer to the question of Fornæss and Sibony, and proves the Binder-DeMarco Conjecture. |
| title | Dimension of equilibrium measures for complex maps |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2402.07001 |