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The Loewner equation describes the time development of an analytic map intothe upper half of the complex plane in the presence of a "forcing", a definedsingularity moving around the real axis. The applications of this equation usethe trace, the locus of singularities in the upper half plane. This notediscusses the structure of the trace for the case in which the forcingfunction, xi(t), is proportional to (-t)^beta with beta in the interval (0,1/2). In this case, the trace is a simple curve, gamma(t), which touches thereal axis twice. It is computed by using matched asymptotic analysis to computethe trajectory of the Loewner evolution in the neighborhood of the singularity,and then assuming a smooth mapping of these trajectories away from thesingularity. Near the t=0 singularity, the trace has a shape given by  [ Re(gamma(t)-gamma(0)) ]^(1-beta) ~ [ beta*Im(gamma(t)) ]^beta ~O(xi(t))^(1-beta).  A numerical calculation of the trace provides support for the asymptotictheory.Comment: 21 pages, 6 figures, submitted to Nonlinearit

Trace for the Loewner equation with singular forcing