Positively Continuum-Wise Expansiveness for C 1 Differentiable Maps

Manseob Lee
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Manseob Lee: Department of Mathematics, Mokwon University, Daejeon 302-729, Korea

Mathematics, 2019, vol. 7, issue 10, 1-8

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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