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Fixed point indices of planar continuous maps

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Hernández Corbato, Luis and Romero Ruiz del Portal, Francisco (2015) Fixed point indices of planar continuous maps. Discrete and Continuous Dynamical Systems. Series A., 35 (7). pp. 2979-2995. ISSN 1078-0947

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Official URL: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10784


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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.


Item Type:Article
Uncontrolled Keywords:Fixed point index; Conley index; isolating blocks; surface homeomorphisms; Lefschetz zeta function
Subjects:Sciences > Mathematics
ID Code:29479
Deposited On:13 Apr 2015 10:59
Last Modified:12 Dec 2018 15:12

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