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Rate of Convergence at the Denjoy-Wolff Point

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Continuous Semigroups of Holomorphic Self-maps of the Unit Disc

Abstract

The aim of this chapter is to study the rate, or speed, of convergence of orbits of non-elliptic semigroups to the Denjoy-Wolff point, considering both “orthogonal speed” and “total speed” as introduced in Definition 6.5.6. As we see, in the hyperbolic case the speed of convergence follows strict rules, while, in the parabolic case the situation is more complicated.

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Correspondence to Filippo Bracci .

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Bracci, F., Contreras, M.D., Díaz-Madrigal, S. (2020). Rate of Convergence at the Denjoy-Wolff Point. 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_16

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