Geodesic
Siegel disks of the tangent family
Weiwei Cui1 ; Hongming Nie2
1 Fudan University, Shanghai Center for Mathematical Sciences and Lund University, Centre for Mathematical Sciences
2 The Hebrew University of Jerusalem, Einstein Institute of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 593-600 Cet article a éte moissonné depuis la source Journal.fi

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We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a Siegel disk is unbounded if and only if the boundary of its image contains at least one asymptotic value. Moreover, by using quasiconformal surgery we also construct functions in the above family with bounded Siegel disks.
Keywords: Meromorphic functions, tangent family, Siegel disks, quasiconformal surgery

Weiwei Cui 1 ; Hongming Nie 2

1 Fudan University, Shanghai Center for Mathematical Sciences and Lund University, Centre for Mathematical Sciences
2 The Hebrew University of Jerusalem, Einstein Institute of Mathematics 
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Weiwei Cui; Hongming Nie. Siegel disks of the tangent family. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 593-600. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a36/