TY  - JOUR
A1  - Kourou, Maria
A1  - Zarvalis, Konstantinos
T1  - Compact sets in petals and their backward orbits under semigroups of holomorphic functions
JF  - Potential Analysis
N2  - Let (ϕ\(_t\))\(_{t≥0}\) 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.
KW  - semigroup of holomorphic functions
KW  - backward orbit
KW  - petal
KW  - harmonic measure
KW  - condenser capacity
KW  - Koenigs function
KW  - green energy
KW  - hyperbolic area
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-324368
SN  - 0926-2601
VL  - 59
IS  - 4
ER  -