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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.03076 |
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| _version_ | 1866912625012506624 |
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| author | Abate, Marco |
| author_facet | Abate, Marco |
| contents | This paper, based upon an unpublished manuscript by Maurice Heins, answers a question posed by Valiron about the dynamics of parabolic self-maps of the unit disk in the complex plane, considerably simplifying arguments previously used for answering the same question. The main new tool introduced is the notion of left straightening of a sequence of iterates, that can be effectively employed for studying the hyperbolic step of a parabolic map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parabolic dynamics according to Maurice Heins Abate, Marco Complex Variables Dynamical Systems 30D05, 37F99 This paper, based upon an unpublished manuscript by Maurice Heins, answers a question posed by Valiron about the dynamics of parabolic self-maps of the unit disk in the complex plane, considerably simplifying arguments previously used for answering the same question. The main new tool introduced is the notion of left straightening of a sequence of iterates, that can be effectively employed for studying the hyperbolic step of a parabolic map. |
| title | Parabolic dynamics according to Maurice Heins |
| topic | Complex Variables Dynamical Systems 30D05, 37F99 |
| url | https://arxiv.org/abs/2509.03076 |