2000 character limit reached
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.