Dubrovnik VI – Geometric Topology

September 30 – October 7, 2007


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Francisco R. Ruiz del Portal*
Universidad Complutense de Madrid, Madrid, Spain

On the growth of the sequence of indices of the iterates of $\R^3$-homeomorphisms

Given a homeomorphism $f:\R^3\to\R^3$ such that $Fix(f)=Per(f)=\{ 0\}$, we will discuss in geometric dynamical terms the behavior of the sequence $\{i(f^m,0)\}_{m \in \N}$ of the fixed point indices of its iterates at 0. We shall comment, from this point of view, some of the most important known results in this topic.

REFERENCES

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[13] F. R. Ruiz del Portal, J. M. Salazar. Fixed point indices of the iterates of $\R^3$-homeomorphisms at Lyapunov stable fixed points, Journal of Diff. Equations (to appear).
[14] F. R. Ruiz del Portal, J. M. Salazar. Fixed point indices of the iterations of $\R^3$-homeomorphisms, preprint.
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* This is a joint work with José Manuel Salazar.

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