On ${\mathrm{C}}^1$-class local diffeomorphisms whose periodic points are nonuniformly expanding

Abstract

Using a sifting-shadowing combination, we prove in this paper that an arbitrary ${\mathrm{C}}^1$-class local diffeomorphism $f$ of a closed manifold $M^n$ is uniformly expanding on the closure ${\mathrm{Cl}}_{M^n}(\mathrm{Per}(f))$ of its periodic point set $\mathrm{Per}(f)$, if it is nonuniformly expanding on $\mathrm{Per}(f)$.

24 pages; accepted by Math. Z

References in corpus (1)

• Shadowing by non uniformly hyperbolic periodic points and uniform hyperbolicity