Basins of attraction in Loewner equations
Abstract
We prove that any Loewner PDE whose driving term h(z,t) vanishes at the origin, and satisfies the bunching condition r m(Dh(0,t))≥ k(Dh(0,t)) for some r∈ R+, admits a solution given by univalent mappings (ft: Bq Cq). This is done by discretizing time and considering the abstract basin of attraction. If r<2, then the union of the images ft(q) of a such solution is biholomorphic to Cq.
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