Abstract
In this chapter, we continue the analysis of the boundary behavior of semigroups, and we concentrate on boundary fixed points. We show that if a positive iterate of a semigroup has a boundary fixed point (in the sense of non-tangential limit), then such a point is indeed fixed for all the iterates of the semigroup. Moreover, the boundary dilation coefficients of the semigroup at a boundary fixed point are either identically infinity or they are of the form \(e^{-\lambda t}\) for some \(\lambda \in \mathbb R\). The latter is the case of boundary regular fixed points. We prove that there is a one-to-one correspondence between boundary regular fixed points and boundary regular critical points of infinitesimal generators.
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Bracci, F., Contreras, M.D., Díaz-Madrigal, S. (2020). Boundary Fixed Points and Infinitesimal Generators. In: Continuous Semigroups of Holomorphic Self-maps of the Unit Disc. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-36782-4_12
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DOI: https://doi.org/10.1007/978-3-030-36782-4_12
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-36781-7
Online ISBN: 978-3-030-36782-4
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