• 제목/요약/키워드: limit property

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VARIOUS SHADOWING PROPERTIES FOR TIME VARYING MAPS

  • Sarkooh, Javad Nazarian
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.481-506
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    • 2022
  • This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.

POSITIVELY EXPANSIVE MAPS AND THE LIMIT SHADOWING PROPERTIES

  • Sakai, Kazuhiro
    • Journal of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.207-218
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    • 2021
  • In this paper, the notion of two-sided limit shadowing property is considered for a positively expansive open map. More precisely, let f be a positively expansive open map of a compact metric space X. It is proved that if f is topologically mixing, then it has the two-sided limit shadowing property. As a corollary, we have that if X is connected, then the notions of the two-sided limit shadowing property and the average-shadowing property are equivalent.

SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES

  • Tsegmid, Nyamdavaa
    • Journal of the Chungcheong Mathematical Society
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    • v.31 no.4
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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.

ON STRONG EXPONENTIAL LIMIT SHADOWING PROPERTY

  • Darabi, Ali
    • Communications of the Korean Mathematical Society
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    • v.37 no.4
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    • pp.1249-1258
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    • 2022
  • In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

TRANSITIVITY, TWO-SIDED LIMIT SHADOWING PROPERTY AND DENSE ω-CHAOS

  • Oprocha, Piotr
    • Journal of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.837-851
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    • 2014
  • We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

Fixed Point Theorems for Weakly Compatible Functions using (JCLR) Property in Intuitionistic Fuzzy Metric Space

  • Park, Jong Seo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.12 no.4
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    • pp.296-299
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    • 2012
  • In this paper, we give definitions for common limit in the range property of mappings and obtain common fixed point theorem for a pair of weakly compatible functions in intuitionistic fuzzy metric space using the joint common limit in the range property of mappings(shortly, (JCLR) property). Our results improve and generalize results of Chauhan et al[1].

ON THE ERGODIC SHADOWING PROPERTY THROUGH UNIFORM LIMITS

  • Namjip Koo;Hyunhee Lee
    • Journal of the Chungcheong Mathematical Society
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    • v.37 no.2
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    • pp.75-80
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    • 2024
  • In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

EMPLOYING COMMON LIMIT RANGE PROPERTY WITH VARIANTS OF R-WEAKLY COMMUTING MAPPINGS IN METRIC SPACES

  • CHAUHAN, SUNNY;VUJAKOVIC, JELENA;HAQ, SHAMSUL
    • The Pure and Applied Mathematics
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    • v.22 no.2
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    • pp.127-138
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    • 2015
  • The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 24(2) (2008), 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying $\phi$-contractive condition.

LIMIT SETS OF POINTS WHOSE STABLE SETS HAVE NONEMPTY INTERIOR

  • Koo, Ki-Shik
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.3
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    • pp.343-348
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    • 2007
  • In this paper, we show that if a homeomorphism has the pseudo-orbit-tracing-property and its nonwandering set is locally connected, then the limit sets of wandering points whose stable sets have nonempty interior consist of single periodic orbit.

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