Positively Continuum-Wise Expansiveness for <i>C</i>¹ Differentiable Maps

Abstract

We show that if a differentiable map f of a compact smooth Riemannian manifold M is C 1 robustly positive continuum-wise expansive, then f is expanding. Moreover, C 1 -generically, if a differentiable map f of a compact smooth Riemannian manifold M is positively continuum-wise expansive, then f is expanding.

Keywords

• positively expansive
• positively measure expansive
• generic
• positively continuum-wise expansive
• expanding