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

Abstract

Given any positive sequence {c n } n∈N , we construct orientation preserving homeomorphisms f : R 3 → R 3 such that Fix(f ) = Per(f ) = {0}, 0 is Lyapunov stable and lim sup |i(f m ,0)| c m = ∞. 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.