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

del Portal, Francisco R. Ruiz; Salazar, José Manuel

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

Authors

Description

Given any positive sequence (\{c_n\}_{n \in {\Bbb N}}), we construct orientation 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 some strong differences with respect to the computation and behavior of the sequences of the indices of planar homeomorphisms.
19 pages, 8 figures