Geodesic
Minimal number of periodic points for smooth self-maps of $S^3$
Grzegorz Graff 1   ; Jerzy Jezierski 2
1 Faculty of Applied Physics and Mathematics Gdańsk University of Technology Narutowicza 11/12 80-233 Gdańsk, Poland
2 Faculty of Applied Informatics and Mathematics Warsaw University of Life Sciences (SGGW) Nowoursynowska 159 00-757 Warszawa, Poland
Fundamenta Mathematicae, Tome 204 (2009) no. 2, pp. 127-144 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $f$ be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension $m\geq 3$ and $r$ a fixed natural number. A topological invariant $D^m_r[f]$, introduced by the authors [Forum Math. 21 (2009)], is equal to the minimal number of $r$-periodic points for all smooth maps homotopic to $f$. In this paper we calculate $D^3_r[f]$ for all self-maps of $S^3$.
DOI : 10.4064/fm204-2-3
Keywords: continuous self map smooth compact connected simply connected manifold dimension geq fixed natural number topological invariant f introduced authors forum math equal minimal number r periodic points smooth maps homotopic paper calculate self maps

Grzegorz Graff  1   ; Jerzy Jezierski  2

1 Faculty of Applied Physics and Mathematics Gdańsk University of Technology Narutowicza 11/12 80-233 Gdańsk, Poland
2 Faculty of Applied Informatics and Mathematics Warsaw University of Life Sciences (SGGW) Nowoursynowska 159 00-757 Warszawa, Poland 
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 smooth self-maps of $S^3$},
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Grzegorz Graff; Jerzy Jezierski. Minimal number of periodic points for
 smooth self-maps of $S^3$. Fundamenta Mathematicae, Tome 204 (2009) no. 2, pp. 127-144. doi: 10.4064/fm204-2-3

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