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Archiv der Mathematik

, Volume 110, Issue 6, pp 617–627 | Cite as

Fixed point indices of iterates of a low-dimensional diffeomorphism at a fixed point which is an isolated invariant set

  • Grzegorz GraffEmail author
Open Access
Article

Abstract

Let f be an \({\mathbb {R}}^n\)-diffeomorphism, where \(n=2,3\), for which \(\{0\}\) is an isolated invariant set. We determine all possible forms of the sequences of fixed point indices of iterates of f at 0, \(\{\mathrm{ind}(f^n, 0)\}_n\), confirming in \({\mathbb {R}}^3\) the conjecture of Ruiz del Portal and Salazar (J Differ Equ 249, 989–1013, 2010).

Keywords

Fixed point index Diffeomorphisms Low-dimensional dynamics Iterates 

Mathematics Subject Classification

Primary 37C25 55M20 Secondary 37C05 

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Faculty of Applied Physics and MathematicsGdańsk University of TechnologyGdańskPoland

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