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arXiv · 1605.08716

Fixed point indices of planar continuous maps

Luis Hernandez-Corbato·Francisco R. Ruiz del Portal
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Abstract

We characterize the sequences of fixed point indices $\{i(f^n, p)\}_{n\ge 1}$ of fixed points that are isolated as an invariant set and continuous maps in the plane. In particular, we prove that the sequence is periodic and $i(f^n, p) \le 1$ for every $n \ge 1$. This characterization allows us to compute effectively the Lefschetz zeta functions for a wide class of continuous maps in the 2-sphere, to obtain new results of existence of infinite periodic orbits inspired on previous articles of J. Franks and to give a partial answer to a problem of Shub about the growth of the number of periodic orbits of degree--$d$ maps in the 2-sphere.

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Luis Hernandez-Corbato, Francisco R. Ruiz del Portal. 2016-05-27. Fixed point indices of planar continuous maps. https://doi.org/10.3934/dcds.2015.35.2979

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