• Title/Summary/Keyword: equicontinuous

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RECURRENCE AND STABILITY OF POINTS IN DISCRETE FLOWS

  • KOO, KI-SHIK
    • Journal of applied mathematics & informatics
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    • v.37 no.3_4
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    • pp.251-257
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    • 2019
  • We study the orbit behaviours of recurrent, uniformly recurrent and Poisson stable points. we give conditons that a point is to be recurrent or uniformly recurrent by analyzing the behaviours of their orbits. Also, we study dynamical properties of equicontinuous points and points of characteristic $0^+$.

POSITIVELY EQUICONTINUOUS FLOWS ARE TOPOLOGICALLY CONJUGATE TO ROTATION FLOWS

  • Bae, Jong-Sook;Min, Kyung-Jin;Sung, Duk-Hyon;Yang, Seung-Kab
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.707-716
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    • 1999
  • In this pater we study the continuity of rotation numbers of liftings of circle maps with degree one. And apply our result to prove that a positively equicontinuous flow of homeomorphisms on the circle $S^1$ is topologically conjugate to a continuous flow of rotation maps.

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ON CHARACTERISTIC 0 AND WEAKLY ALMOST PERIODIC FLOWS

  • Song, Hyungsoo
    • Korean Journal of Mathematics
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    • v.11 no.2
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    • pp.161-167
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    • 2003
  • The purpose of this paper is to study and characterize the notions of characteristic 0 and weakly almost periodicity in flows. In particular, we give sufficient conditions for the weakly almost periodic flow to be almost periodic.

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Asymptotics in Transformed ARMA Models

  • Yeo, In-Kwon
    • Communications for Statistical Applications and Methods
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    • v.18 no.1
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    • pp.71-77
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    • 2011
  • In this paper, asymptotic results are investigated when a parametric transformation is applied to ARMA models. The conditions are determined to ensure the strong consistency and the asymptotic normality of maximum likelihood estimators and the correct coverage probability of the forecast interval obtained by the transformation and backtransformation approach.

TOPOLOGICAL COMPLEXITY OF SEMIGROUP ACTIONS

  • Yan, Xinhua;He, Lianfa
    • Journal of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.221-228
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    • 2008
  • In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.

COMPLEXITY OF CONTINUOUS SEMI-FLOWS AND RELATED DYNAMICAL PROPERTIES

  • Zhang, Feng;He, Lian-Fa;Lu, Qi-Shao
    • Journal of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.225-236
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    • 2009
  • The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.

RELATIVE SEQUENCE ENTROPY PAIRS FOR A MEASURE AND RELATIVE TOPOLOGICAL KRONECKER FACTOR

  • AHN YOUNG-HO;LEE JUNGSEOB;PARK KYEWON KOH
    • Journal of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.857-869
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    • 2005
  • Let $(X,\;B,\;{\mu},\;T)$ be a dynamical system and (Y, A, v, S) be a factor. We investigate the relative sequence entropy of a partition of X via the maximal compact extension of (Y, A, v, S). We define relative sequence entropy pairs and using them, we find the relative topological ${\mu}-Kronecker$ factor over (Y, v) which is the maximal topological factor having relative discrete spectrum over (Y, v). We also describe the topological Kronecker factor which is the maximal factor having discrete spectrum for any invariant measure.