We show that an evolution family of the unit disc is commuting if and only if the associated Herglotz vector field has separated variables. This is the case if and only if the evolution family comes from a semigroup of holomorphic self-maps of the disc.
Semigroups versus evolution families in the Loewner theory / BRACCI, FILIPPO; Contreras, M; Diaz Madrigal, S.. - In: JOURNAL D'ANALYSE MATHEMATIQUE. - ISSN 0021-7670. - 115:(2011), pp. 273-292. [10.1007/s11854-011-0030-y]
Semigroups versus evolution families in the Loewner theory
BRACCI, FILIPPO;
2011
Abstract
We show that an evolution family of the unit disc is commuting if and only if the associated Herglotz vector field has separated variables. This is the case if and only if the evolution family comes from a semigroup of holomorphic self-maps of the disc.
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