David extension of circle homeomorphisms, welding, mating, and removability
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911166572265472 |
|---|---|
| author | Lyubich, Mikhail Merenkov, Sergei Mukherjee, Sabyasachi Ntalampekos, Dimitrios |
| author_facet | Lyubich, Mikhail Merenkov, Sergei Mukherjee, Sabyasachi Ntalampekos, Dimitrios |
| contents | We provide a David extension result for circle homeomorphisms conjugating two dynamical systems such that parabolic periodic points go to parabolic periodic points, but hyperbolic points can go to parabolics as well. We use this result, in particular, to prove the existence of a new class of welding homeomorphisms, to establish an explicit dynamical connection between critically fixed anti-rational maps and kissing reflection groups, to show conformal removability of the Julia sets of geometrically finite polynomials and of the limit sets of necklace reflection groups, to produce matings of anti-polynomials and necklace reflection groups, and to give a new proof of the existence of Suffridge polynomials (extremal points in certain spaces of univalent maps). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_11256 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | David extension of circle homeomorphisms, welding, mating, and removability Lyubich, Mikhail Merenkov, Sergei Mukherjee, Sabyasachi Ntalampekos, Dimitrios Dynamical Systems Complex Variables 30C50, 30C62, 30C75, 30D05, 30J10, 37F10, 37F31, 37F32, 51F15 We provide a David extension result for circle homeomorphisms conjugating two dynamical systems such that parabolic periodic points go to parabolic periodic points, but hyperbolic points can go to parabolics as well. We use this result, in particular, to prove the existence of a new class of welding homeomorphisms, to establish an explicit dynamical connection between critically fixed anti-rational maps and kissing reflection groups, to show conformal removability of the Julia sets of geometrically finite polynomials and of the limit sets of necklace reflection groups, to produce matings of anti-polynomials and necklace reflection groups, and to give a new proof of the existence of Suffridge polynomials (extremal points in certain spaces of univalent maps). |
| title | David extension of circle homeomorphisms, welding, mating, and removability |
| topic | Dynamical Systems Complex Variables 30C50, 30C62, 30C75, 30D05, 30J10, 37F10, 37F31, 37F32, 51F15 |
| url | https://arxiv.org/abs/2010.11256 |