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About the homological discrete Conley index of isolated invariant acyclic continua

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Hernández Corbato, Luis and Le Calvez , Patrice and Romero Ruiz del Portal, Francisco (2013) About the homological discrete Conley index of isolated invariant acyclic continua. Geometry & topology, 17 (5). pp. 2977-3026. ISSN 1465-3060

Official URL: http://www.msp.warwick.ac.uk/gt/2013/17-05/p066.xhtml



Abstract

This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a locally defined homeomorphism f in R-d and an acyclic continuum X, such as a cellular set or a fixed point, invariant under f and isolated. We prove that the trace of the first discrete homological Conley index of f and X is greater than or equal to -1 and describe its periodical behavior. If equality holds then the traces of the higher homological indices are 0. In the case of orientation-reversing homeomorphisms of R-3, we obtain a characterization of the fixed point index sequence {i(f(n) (,) p}n >= 1 for a fixed point p which is isolated as an invariant set. In particular, we obtain that i(f , p) <= 1. As a corollary, we prove that there are no minimal orientation-reversing homeomorphisms in R-3.


Item Type:Article
Uncontrolled Keywords:Fixed-point index; dynamical-systems; homeomorphisms; theorem; plane; maps
Subjects:Sciences > Mathematics > Geometry
ID Code:24157
Deposited On:09 Jan 2014 12:46
Last Modified:12 Dec 2018 15:12

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