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Self-maps of S 2 homotopic to a smooth map with a single n-periodic point

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Abstract

We show for which (d, n) ∈ ℤ × ℕ there exists a smooth self-map f: S 2 → S 2 so that deg(f) = d and Fix(f n) is a point.

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Authors and Affiliations

  1. Department of Applied Informatics and Mathematics, Warsaw University of Life Sciences, Nowoursynowska 159, 02757, Warszawa, Poland

    Jerzy Jezierski

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  1. Jerzy Jezierski
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Correspondence to Jerzy Jezierski.

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Supported by the National Science Centre, Poland (Grant No. UMO-2014/15/B/ST1/01710)

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Jezierski, J. Self-maps of S 2 homotopic to a smooth map with a single n-periodic point. Acta. Math. Sin.-English Ser. 33, 1073–1082 (2017). https://doi.org/10.1007/s10114-017-6120-8

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  • DOI: https://doi.org/10.1007/s10114-017-6120-8

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