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).
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Research supported by the National Science Center, Poland, UMO-2014/15/B/ST1/01710.
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Graff, G. Fixed point indices of iterates of a low-dimensional diffeomorphism at a fixed point which is an isolated invariant set. Arch. Math. 110, 617–627 (2018). https://doi.org/10.1007/s00013-018-1180-2
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DOI: https://doi.org/10.1007/s00013-018-1180-2