• 제목/요약/키워드: asymptotic average shadowing

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VARIOUS SHADOWING PROPERTIES FOR INVERSE LIMIT SYSTEMS

  • Lee, Manseob
    • 충청수학회지
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    • 제29권4호
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    • pp.657-661
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    • 2016
  • Let $f:X{\rightarrow}X$ be a continuous surjection of a compact metric space and let ($X_f,{\tilde{f}}$) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f, if f has the asymptotic average, the average shadowing, the ergodic shadowing property then ${\tilde{f}}$ is topologically transitive.

SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES

  • Tsegmid, Nyamdavaa
    • 충청수학회지
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    • 제31권4호
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    • pp.461-466
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    • 2018
  • $Let\;f:X{\rightarrow}X$ be a continuous surjection of a compact metric space X and let ${\sigma}_f:X_f{\rightarrow}X_f$ be the shift map on the inverse limit space $X_f$ constructed by f. We show that if a continuous surjective map f has some shadowing properties: the asymptotic average shadowing property, the average shadowing property, the two side limit shadowing property, then ${\sigma}_f$ also has the same properties.

ASYMPTOTIC AVERAGE SHADOWING PROPERTY ON A CLOSED SET

  • Lee, Manseob;Park, Junmi
    • 충청수학회지
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    • 제25권1호
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    • pp.27-33
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    • 2012
  • Let $f$ be a difeomorphism of a closed $n$ -dimensional smooth manifold M, and $p$ be a hyperbolic periodic point of $f$. Let ${\Lambda}(p)$ be a closed set which containing $p$. In this paper, we show that (i) if $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$, then ${\Lambda}(p)$ is the chain component which contains $p$. (ii) suppose $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$. Then if $f|_{\Lambda(p)}$ has the $C^{1}$-stably shadowing property then it is hyperbolic.

SOME PROPERTIES OF STRONG CHAIN TRANSITIVE MAPS

  • Barzanouni, Ali
    • 대한수학회논문집
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    • 제34권3호
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    • pp.951-965
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    • 2019
  • Let $f:X{\rightarrow}X$ be a continuous map on a compact metric space (X, d) and for an arbitrary $x{\in}X$, $${\mathcal{SC}}_d(x,f):=\{y{\mid}x{\text{ can be strong }}d-{\text{chain to }}y\}$$. We give an example to show that ${\mathcal{SC}}_d(x,f)$ is dependent on the metric d on X but it is a closed and f-invariant set. We prove that if ${\mathcal{SC}}_d(x,f){\supseteq}{\Omega}(f)$ or f has the asymptotic-average shadowing property, then ${\mathcal{SC}}_d(x,f)=X$. Also, we show that if f has the shadowing property, then ${\lim}\;{\sup}_{n{\in}{\mathbb{N}}}\{f^n\}={\mathcal{SC}}_d(f)$ where ${\mathcal{SC}}_d(f)=\{(x,y){\mid}y{\in}{\mathcal{SC}}_d(x,f)\}$. For each $n{\in}{\mathbb{N}}$, we give an example in which ${\mathcal{SCR}}_d(f^n){\neq}{\mathcal{SCR}}_d(f)$. In spite of it, we prove that if $f^{-1}:(X,d){\rightarrow}(X,d)$ is an equicontinuous map, then ${\mathcal{SCR}}_d(f^n)={\mathcal{SCR}}_d(f)$ for all $n{\in}{\mathbb{N}}$.

Achievable Sum Rate Analysis of ZF Receivers in 3D MIMO Systems

  • Li, Xingwang;Li, Lihua;Xie, Ling
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제8권4호
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    • pp.1368-1389
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    • 2014
  • Three-dimensional multiple-input multiple-output (3D MIMO) and large-scale MIMO are two promising technologies for upcoming high data rate wireless communications, since the inter-user interference can be reduced by exploiting antenna vertical gain and degree of freedom, respectively. In this paper, we derive the achievable sum rate of 3D MIMO systems employing zero-forcing (ZF) receivers, accounting for log-normal shadowing fading, path-loss and antenna gain. In particular, we consider the prevalent log-normal model and propose a novel closed-form lower bound on the achievable sum rate exploiting elevation features. Using the lower bound as a starting point, we pursue the "large-system" analysis and derive a closed-form expression when the number of antennas grows large for fixed average transmit power and fixed total transmit power schemes. We further model a high-building with several floors. Due to the floor height, different floors correspond to different elevation angles. Therefore, the asymptotic achievable sum rate performances for each floor and the whole building considering the elevation features are analyzed and the effects of tilt angle and user distribution for both horizontal and vertical dimensions are discussed. Finally, the relationship between the achievable sum rate and the number of users is investigated and the optimal number of users to maximize the sum rate performance is determined.