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- 주제어 : expansive (검색결과 5,178 건)
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Various expansive measures for flows
Lee, Keonhee,Morales, C.A.,Nguyen, Ngoc-Thach Elsevier 2018 Journal of differential equations Vol.265 No.5
<P><B>Abstract</B></P> <P>We discuss a characterization of countably expansive flows in measure-theoretical terms as in the discrete case . More precisely, we define the <I>countably expansive flows</I> and prove that a homeomorphism of a compact metric space is countable expansive just when its suspension flow is. Moreover, we exhibit a measure-expansive flow (in the sense of ) which is not countably expansive. Next we define the weak expansive measures for flows and prove that a flow of a compact metric space is countable expansive if and only if it is <I>weak measure-expansive</I> (i.e. every orbit-vanishing measure is weak expansive). Furthermore, unlike the measure-expansive ones, the weak measure-expansive flows may exist on closed surfaces. Finally, it is shown that the integrated flow of a <SUP> C 1 </SUP> vector field on a compact smooth manifold is <SUP> C 1 </SUP> stably expansive if and only if it is <SUP> C 1 </SUP> stably weak measure-expansive.</P>
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TOPOLOGICAL ENTROPY OF EXPANSIVE FLOW ON TVS-CONE METRIC SPACES
Kyung Bok Lee 충청수학회 2021 충청수학회지 Vol.34 No.3
We shall study the following. Let phi be an expansive flow on a compact TVS-cone metric space (X,d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that limsup {1over t} log v(t) le h(phi), where v(t) denotes the number of closed orbits of phi with a period tau in [0,t] and h(phi) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space
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Positively weak measure expansive differentiable maps
안지원,이만섭 대한수학회 2020 대한수학회보 Vol.57 No.3
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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POSITIVELY WEAK MEASURE EXPANSIVE DIFFERENTIABLE MAPS
Ahn, Jiweon,Lee, Manseob Korean Mathematical Society 2020 대한수학회보 Vol.57 No.3
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<sup>1</sup>-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 C<sup>1</sup>-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C<sup>1</sup>-generic f ∈ C<sup>1</sup> (M), f is positively weak measure-expansive if and only if f is expanding.
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SYMBOLICALLY EXPANSIVE DYNAMICAL SYSTEMS
오주미 충청수학회 2022 충청수학회지 Vol.35 No.1
In this article, we consider the notion of expansiveness on compact metric spaces for symbolically point of view. And we show that a homeomorphism is symbolically countably expansive if and only if it is symbolically measure expansive. Moreover, we prove that a homeomorphism is symbolically N-expansive if and only if it is symbolically measure N-expanding.
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ENTROPY MAPS FOR MEASURE EXPANSIVE HOMEOMORPHISMS
Jaehyun Jeong,Woochul Jung 충청수학회 2015 충청수학회지 Vol.28 No.3
It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.
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Weak measure expansiveness for partially hyperbolic diffeomorphisms
Elsevier 2017 Chaos, solitons, and fractals Vol.103 No.-
<P><B>Abstract</B></P> <P>Let <I>M</I> be a closed connected smooth Riemannian manifold with dim<I>M</I> ≥ 2 and let <I>f: M</I> → <I>M</I> be a diffeomorphism. In the paper, we show that <I>C</I> <SUP>1</SUP> generically, if a diffeomorphism <I>f</I> does not present a homoclinic tangency then it is weak Lebesgue measure expansive and, as an example, we find a partially hyperbolic diffeomorphism which is not weak measure expansive. Moreover, for a surface, if a diffeomorphism <I>f</I> has a homoclinic tangency then there is a diffeomorphism <I>g C</I> <SUP>1</SUP> close to <I>f</I> such that <I>g</I> is not weak measure expansive.</P>
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ENTROPY MAPS FOR MEASURE EXPANSIVE HOMEOMORPHISM
JEONG, JAEHYUN,JUNG, WOOCHUL Chungcheong Mathematical Society 2015 충청수학회지 Vol.28 No.3
It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.
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Katok-Hasselblatt-kinematic expansive flows
Hien Minh Huynh 대한수학회 2022 대한수학회지 Vol.59 No.1
In this paper we introduce a new notion of expansive flows, which is the combination of expansivity in the sense of Katok and Hasselblatt and kinematic expansivity, named KH-kinematic expansivity. We present new properties of several variations of expansivity. A new hierarchy of expansive flows is given.
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Weak measure expansiveness and chaotic systems
이만섭 충청수학회 2019 충청수학회지 Vol.32 No.4
'In this article, we consider that if a continuous map $f:X\to X$ of a compact metric space $X$ is Li-York chaotic then it is positively weak measure expansive.
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