# Collisions and Spirals of Loewner Traces - Mathematics > Complex Variables

Abstract: We analyze Loewner traces driven by functions asymptotic to K\sqrt{1-t}. Weprove a stability result when K is not 4 and show that K=4 can lead to nonlocally connected hulls. As a consequence, we obtain a driving term \lambdatso that the hulls driven by K\lambdat are generated by a continuous curve forall K > 0 with K not equal to 4 but not when K = 4, so that the space ofdriving terms with continuous traces is not convex. As a byproduct, we obtainan explicit construction of the traces driven by K\sqrt{1-t} and a conceptualproof of the corresponding results of Kager, Nienhuis and Kadanoff,math-ph-0309006

Author: Joan Lind, Donald E. Marshall, Steffen Rohde

Source: https://arxiv.org/