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 $f \colon \mathbb{R}^d\to \mathbb{R}^d$, $d \ge 2$, such that ${\rm Per}(f) ={\rm Fix}(f) =\{o\}$, where $o$ denotes the origin, and $(i(f^n, o))_n = I$.