Siegel disks of the tangent family
Abstract
We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a forward invariant Siegel disk is unbounded if and only if it contains at least one asymptotic value on the boundary. Our argument is elementary and function-theoretic. Moreover, by using quasiconformal surgery we also construct functions in the above family with bounded Siegel disks.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2019
- DOI:
- 10.48550/arXiv.1906.06802
- arXiv:
- arXiv:1906.06802
- Bibcode:
- 2019arXiv190606802C
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Complex Variables;
- 30D05;
- 37F10
- E-Print:
- V2: 10 pages, 1 figure, overall revision in the introduction, main result extends to all periods