Indices of fixed points not accumulated by periodic points

Abstract

We prove that for every integer sequence $I$ satisfying Dold relations there exists a map $f:{\mathbb{R}}^d\to {\mathbb{R}}^d$, $d\ge 2$, such that $\mathrm{Per}(\mathrm{f})=\mathrm{Fix}(\mathrm{f})=\{o\}$, where $o$ denotes the origin, and $(i(f^n,o){)}_n=I$.

11 pages, 2 figures. Final version to appear in Topol. Methods Nonlinear Anal