A generalization of the Bowen-York initial data to the case with a positive
cosmological constant is investigated. We follow the construction presented
recently by Bizo\'n, Pletka and Simon, and solve numerically the Lichnerowicz
equation on a compactified domain S1Ă—S2. In addition
to two branches of solutions depending on the polar variable on S2
that were already known, we find branches of solutions depending on two
variables: the polar variable on S2 and the coordinate on S1. Using Vanderbauwhede's results concerning bifurcations from symmetric
solutions, we show the existence of the corresponding bifurcation points. By
linearizing the Lichnerowicz equation and solving the resulting eigenvalue
problem, we collect numerical evidence suggesting the absence of additional
branches of solutions.Comment: 24 pages, 9 figure