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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 $C^1$-differentiable maps on a compact smooth manifold $M$. And we prove that the following theorems. \begin{itemize} \item[(1)] Let $\mathcal{PWE}$ be the set of all positively weak measure expansive differentiable maps of $M$. Denote by $\rm{int}(\mathcal{PWE})$ is a $C^1$-interior of $\mathcal{PWE}$. $f \in\rm{int}(\mathcal{PWE})$ if and only if $f$ is expanding. \item[(2)] For $C^1$-{\it generic} $f \in C^1(M)$, $f$ is positively weak measure-expansive if and only if $f$ is expanding. \end{itemize}
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참고문헌 (16)
참고문헌 신청
안지원 / 2018 / Stability of weak measure expansive diffeomorphisms / 대한수학회지 55(5):1131~1142
안지원 / 2014 / Positively measure expansive and expanding / 대한수학회논문집 29(2):345~349
N. Aoki / 2001 / C1-maps having hyperbolic periodic points / Fundamenta Mathematicae 169(1):1~49
Alexander Arbieto / 2011 / Periodic orbits and expansiveness / Mathematische Zeitschrift 269(3-4):801~807
S. Hayashi / 1992 / Diffomorphisms in F1(M)satisfy Axiom A / Ergod. Th. & Dynam. Sys 12:233~253
안지원 / 2014 / Positively measure expansive and expanding / 대한수학회논문집 29(2):345~349
N. Aoki / 2001 / C1-maps having hyperbolic periodic points / Fundamenta Mathematicae 169(1):1~49
Alexander Arbieto / 2011 / Periodic orbits and expansiveness / Mathematische Zeitschrift 269(3-4):801~807
S. Hayashi / 1992 / Diffomorphisms in F1(M)satisfy Axiom A / Ergod. Th. & Dynam. Sys 12:233~253
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