• Bulletin of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.569-581
• /
• 2020

In this paper, we introduce the new general concept of usual expansiveness which is called "positively weak measure expansiveness" and study the basic properties of positively weak measure expansive C¹-differentiable maps on a compact smooth manifold M. And we prove that the following theorems. (1) Let 𝓟𝓦𝓔 be the set of all positively weak measure expansive differentiable maps of M. Denote by int(𝓟𝓦𝓔) is a C¹-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C¹-generic f ∈ C¹ (M), f is positively weak measure-expansive if and only if f is expanding.

• Communications of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.345-349
• /
• 2014

We show that $C^1$-generically, a differentiable map is positively measure expansive if and only if it is expanding.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.1
• /
• pp.151-155
• /
• 2014

In this paper, we introduce some examples of measure expansive maps.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.4
• /
• pp.461-464
• /
• 2019

In this article, we consider that if a continuous map f : X → X of a compact metric space X is Li-York chaotic then it is positively weak measure expansive.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.257-267
• /
• 1997

It is shown that if S is a positively expansive endomorphism on a one-sided mixing SFT (X,T), then (X,S) is conjugate to a one-sided mixing SFT, and the Parry measures of (X,T) and (X,S) are identical.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.4
• /
• pp.647-651
• /
• 2015

Let (X, d) be a compact metric space, and let $f:X{\rightarrow}X$ be a continuous map. We consider that if a positively continuum-wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.