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Basins of attraction in Loewner equations (1108.6000v2)

Published 30 Aug 2011 in math.CV and math.DS

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))\geq k(Dh(0,t)) for some r\in R+, admits a solution given by univalent mappings (f_t: Bq\to Cq). This is done by discretizing time and considering the abstract basin of attraction. If r<2, then the union of the images f_t(\Bq) of a such solution is biholomorphic to Cq.

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