Boundaries of Baker domains of entire functions. A finer approach
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913095603978240 |
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| author | Jové, Anna Pawelec, Łukasz |
| author_facet | Jové, Anna Pawelec, Łukasz |
| contents | We consider transcendental entire functions having doubly parabolic Baker domains, such that the Denjoy-Wolff point of the associated inner function is not a singularity. We describe in a very precise way the dynamics on the boundary from a measure-theoretical point of view. Applications of such results lead to a better understanding of the topology and the dynamics on the boundaries. In particular, we improve some of the results in [N. Fagella and A. Jové, A model for boundary dynamics of Baker domains], for the Baker domain of $z+e^{-z}$. In fact, our conclusions are obtained by applying new results established here on the dynamics of the radial extension of one component doubly parabolic inner functions, which strengthen those of [O. Ivrii and M. Urbański, Inner functions, composition operators, symbolic dynamics and thermodynamic formalism]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05184 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundaries of Baker domains of entire functions. A finer approach Jové, Anna Pawelec, Łukasz Dynamical Systems 37F10, 37A40 We consider transcendental entire functions having doubly parabolic Baker domains, such that the Denjoy-Wolff point of the associated inner function is not a singularity. We describe in a very precise way the dynamics on the boundary from a measure-theoretical point of view. Applications of such results lead to a better understanding of the topology and the dynamics on the boundaries. In particular, we improve some of the results in [N. Fagella and A. Jové, A model for boundary dynamics of Baker domains], for the Baker domain of $z+e^{-z}$. In fact, our conclusions are obtained by applying new results established here on the dynamics of the radial extension of one component doubly parabolic inner functions, which strengthen those of [O. Ivrii and M. Urbański, Inner functions, composition operators, symbolic dynamics and thermodynamic formalism]. |
| title | Boundaries of Baker domains of entire functions. A finer approach |
| topic | Dynamical Systems 37F10, 37A40 |
| url | https://arxiv.org/abs/2605.05184 |