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

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

2007-04-18

arxiv.org/abs/0704.2402v1

Mathematics

Dynamical Systems

19 pages, 8 figures

Scientific paper

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.

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