Indices of the iterates of R3-homeomorphisms at Lyapunov stable fixed points

Given any positive sequence {cn}n∈N, we construct orientation preserving homeomorphisms such that Fix(f)=Per(f)={0}, 0 is Lyapunov stable and . We will use our results to discuss and to point out some strong differences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.