On the growth rate inequality for self-maps of the sphere

Héctor Barge, Luis Hernández-Corbato

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 self--map of $S^m$ such that $f^{-1}(P)=P$ and $|\mathrm{deg}(f_{|P…