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


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).


Fixed point index Diffeomorphisms Low-dimensional dynamics Iterates 

Mathematics Subject Classification

Primary 37C25 55M20 Secondary 37C05 


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© The Author(s) 2018

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Authors and Affiliations

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

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