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arXiv · 1707.06144

On the growth rate inequality for periodic points in the two sphere

G. Honorato·J. Iglesias·A. Portela·A. Rovella·F. Valenzuela·J. Xavier
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Abstract

Let $f:S^2\to S^2$ be a continuous map such that $deg f = d, |d|>1$. Suppose $f$ has two attracting fixed points denoted $N$ and $S$ and let $A=S^2\setminus \{N,S\}$. Assume that if a loop $γ\subset f^{-1}(A)$ is homotopically trivial in $A$, then $f(γ)$ is also homotopically trivial in $A$. Then, for all $n$, $f$ has at least $|d^n -1|$ fixed points.

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G. Honorato, J. Iglesias, A. Portela, A. Rovella, F. Valenzuela, J. Xavier. 2017-07-19. On the growth rate inequality for periodic points in the two sphere. https://arxiv.org/abs/1707.06144

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