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Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we constructorientation preserving homeomorphisms (f:{\Bbb R}^3 \to {\Bbb R}^3) such that(Fix(f)=Per(f)=\{0\}), (0) is Lyapunov stable and (\limsup \frac{|i(f^m,0)|}{c_m}= \infty). We will use our results to discuss and to point out somestrong differences with respect to the computation and behavior of thesequences of the indices of planar homeomorphisms.

Indices of the iterates of $R^3$-homeomorphisms at Lyapunov stable fixed points