On the growth rate inequality for selfmaps of the sphere
Abstract
Let $S^m = \{x_0^2 + x_1^2 + \cdots + x_m^2 = 1\}$ and $P = \{x_0 = x_1 = 0\} \cap S^m$. Suppose that $f$ is a selfmap of $S^m$ such that $f^{1}(P) = P$ and $\mathrm{deg}(f_{P}) < \mathrm{deg}(f)$. Then, the number of fixed points of $f^n$ grows at least exponentially with base $d > 1$, where $d = \mathrm{deg}(f)/\mathrm{deg}(f_{P}) \in \mathbb Z$.
 Publication:

arXiv eprints
 Pub Date:
 January 2023
 DOI:
 10.48550/arXiv.2301.08543
 arXiv:
 arXiv:2301.08543
 Bibcode:
 2023arXiv230108543B
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 10 pages, 1 figure