Selection rules for the tip-splitting instability

The local destabilization of a Saffman-Taylor viscous finger occurs by a splitting of its tip and results in the formation of two branches separated by a fjord. The accumulation of such instabilities leads to complex patterns. In this paper we present a detailed analysis of a dynamical model that accounts for the selection of both the width and the orientation of the fjords growing in a wedge of angle theta(0). It is shown that the selection rules have a dynamical origin and are related to the existence of attracting sets that disappear in the absence of surface tension. We also infer the existence of a critical angle theta(c)=60 degrees such that if theta(0)