On the growth of the number of periodic points for smooth self-maps of a compact manifold

Graff, Grzegorz; Jezierski, Jerzy

doi:10.1090/S0002-9939-07-08836-3

On the growth of the number of periodic points for smooth self-maps of a compact manifold
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by Grzegorz Graff and Jerzy Jezierski PDF

Proc. Amer. Math. Soc. 135 (2007), 3249-3254 Request permission

Abstract:

Let $f$ be a continuous self-map of a smooth compact connected and simply-connected manifold of dimension $m\geq 3$. We show that in the homotopy class of $f$ there is a $C^1$ map with less then $r$ periodic points, up to any given fixed period $r$.

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