Compact Sets in Petals and Their Backward Orbits Under Semigroups of Holomorphic Functions
Tóm tắt
Let (ϕt)t≥ 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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