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arXiv · 2111.15297

Compact Sets in Petals and their Backward Orbits under Semigroups of Holomorphic Functions

Maria Kourou·Konstantinos Zarvalis
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Abstract

Let $(\phi_t)_{t \geq 0}$ be a semigroup of holomorphic functions in the unit disk $\mathbb{D}$ and $K$ a compact subset of $\mathbb{D}$. We investigate the conditions under which the backward orbit of $K$ under the semigroup exists. Subsequently, the geometric characteristics, as well as, potential theoretic quantities for the backward orbit of $K$ are examined. More specifically, results are obtained concerning the asymptotic behavior of its hyperbolic area and diameter, the harmonic measure and the capacity of the condenser that $K$ forms with the unit disk.

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Maria Kourou, Konstantinos Zarvalis. 2021-11-30. Compact Sets in Petals and their Backward Orbits under Semigroups of Holomorphic Functions. https://arxiv.org/abs/2111.15297

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