Publication: Fixed point indices of planar continuous maps
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Publication Date
2015-07
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American Institute of Mathematical Sciences
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Abstract
We characterize the sequences of fixed point indices {i(f(n) ,p)} n >= 1 of fixed points that are isolated as an invariant set for a continuous map f in the plane. In particular, we prove that the sequence is periodic and i(f(n) ,p) <= 1 for every n >= 0. 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 M. Shub about the growth of the number of periodic orbits of degree-d maps in the 2-sphere.