The Centres of Gravity of Periodic Orbits

Abstract

Let $f : I → I$ be a continuous map. If $P(n, f) = \{x ∈ I; f^n (x) = x \}$ is a finite set for each $n ∈ \boldsymbol{N}$, then there exists an anticentered map topologically conjugate to $f$, which partially answers a question of Kolyada and Snoha. Specially, there exists an anticentered map topologically conjugate to the standard tent map.