On the Holomorphic and Random Dynamics for some examples of higher rank Free Groups generated by Hénon type maps
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915768905498624 |
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| author | Santander, Andres Enrique Quintero |
| author_facet | Santander, Andres Enrique Quintero |
| contents | We study the Holomorphic and Random Dynamics of some rank 2 free groups generated by two Hénon type maps. For these simply constructed examples we prove that the Fatou set is non-empty and that the stationary measures are supported on a compact set. With some further care this allows us to construct examples having no stationary measures. These examples illustrate the types of phenomena that may arise when studying holomorphic group actions on non-compact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02324 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Holomorphic and Random Dynamics for some examples of higher rank Free Groups generated by Hénon type maps Santander, Andres Enrique Quintero Dynamical Systems 37F80 (Primary), 37F10, 37H10 We study the Holomorphic and Random Dynamics of some rank 2 free groups generated by two Hénon type maps. For these simply constructed examples we prove that the Fatou set is non-empty and that the stationary measures are supported on a compact set. With some further care this allows us to construct examples having no stationary measures. These examples illustrate the types of phenomena that may arise when studying holomorphic group actions on non-compact manifolds. |
| title | On the Holomorphic and Random Dynamics for some examples of higher rank Free Groups generated by Hénon type maps |
| topic | Dynamical Systems 37F80 (Primary), 37F10, 37H10 |
| url | https://arxiv.org/abs/2602.02324 |