### Minimal number of periodic points for smooth self-maps of two-holed 3-dimensional closed ball

DOI: http://dx.doi.org/10.12775/TMNA.2009.009

#### Abstract

Let $M$ be two-holed $3$-dimensional closed ball, $r$ a given

natural number. We consider $f$, a continuous self-map of $M$ with

real eigenvalues on the second homology group, and determine the

minimal number of $r$-periodic points for all smooth maps

homotopic to $f$.

natural number. We consider $f$, a continuous self-map of $M$ with

real eigenvalues on the second homology group, and determine the

minimal number of $r$-periodic points for all smooth maps

homotopic to $f$.

#### Keywords

Least number of periodic points; Nielsen number; fixed point index; smooth maps

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