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.

V2: 10 pages, 1 figure, overall revision in the introduction, main result extends to all periods

References in corpus (2)

• Stable components in the parameter plane of transcendental functions of finite type
• The high type quadratic Siegel disks are Jordan domains