Weak mixing behavior for the projectivized derivative extension
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916545952743424 |
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| author | Banerjee, Shilpak Khurana, Divya Kunde, Philipp |
| author_facet | Banerjee, Shilpak Khurana, Divya Kunde, Philipp |
| contents | In both smooth and analytic categories, we construct examples of diffeomorphisms of topological entropy zero with intricate ergodic properties. On any smooth compact connected manifold of dimension 2 admitting a nontrivial circle action, we construct a smooth diffeomorphism whose differential is weakly mixing with respect to a smooth measure in the projectivization of the tangent bundle. In case of the 2-torus, we also obtain the analytic counterpart of such a diffeomorphism. The constructions are based on a quantitative version of the ``Approximation by Conjugation'' method, which involves explicitly defined conjugation maps, partial partitions, and the adaptation of a specific analytic approximation technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak mixing behavior for the projectivized derivative extension Banerjee, Shilpak Khurana, Divya Kunde, Philipp Dynamical Systems 37C40, 32C05 In both smooth and analytic categories, we construct examples of diffeomorphisms of topological entropy zero with intricate ergodic properties. On any smooth compact connected manifold of dimension 2 admitting a nontrivial circle action, we construct a smooth diffeomorphism whose differential is weakly mixing with respect to a smooth measure in the projectivization of the tangent bundle. In case of the 2-torus, we also obtain the analytic counterpart of such a diffeomorphism. The constructions are based on a quantitative version of the ``Approximation by Conjugation'' method, which involves explicitly defined conjugation maps, partial partitions, and the adaptation of a specific analytic approximation technique. |
| title | Weak mixing behavior for the projectivized derivative extension |
| topic | Dynamical Systems 37C40, 32C05 |
| url | https://arxiv.org/abs/2412.21041 |