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SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES
Nyamdavaa Tsegmid 충청수학회 2018 충청수학회지 Vol.31 No.4
Let f : X → X be a continuous surjection of a compact metric space X and let 𝜎f : Xf → Xf be the shift map on the inverse limit space Xf 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 𝜎f also has the same properties.
SOME SHADOWING PROPERTIES OF THE SHIFTS ON THE INVERSE LIMIT SPACES
Tsegmid, Nyamdavaa Chungcheong Mathematical Society 2018 충청수학회지 Vol.31 No.4
$Let\;f:X{\rightarrow}X$ 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.
Topological stability in hyperspace dynamical systems
구남집,이현희,Nyamdavaa Tsegmid 대한수학회 2020 대한수학회논문집 Vol.35 No.4
In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.
ON THE DENSITY OF VARIOUS SHADOWING PROPERTIES
Koo, Namjip,Tsegmid, Nyamdavaa Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.3
In this paper we deal with some shadowing properties of discrete dynamical systems on a compact metric space via the density of subdynamical systems. Let $f:X{\rightarrow}X$ be a continuous map of a compact metric space X and A be an f-invariant dense subspace of X. We show that if $f{\mid}_A:A{\rightarrow}A$ has the periodic shadowing property, then f has the periodic shadowing property. Also, we show that f has the finite average shadowing property if and only if $f{\mid}_A$ has the finite average shadowing property.
구남집,이현희,Nyamdavaa Tsegmid 대한수학회 2024 대한수학회보 Vol.61 No.1
In this paper, we consider the set of periodic shadowable points for homeomorphisms of a compact metric space, and we prove that this set satisfies some properties such as invariance and being a $G_{\delta}$ set. Then we investigate implication relations related to sets consisting of shadowable points, periodic shadowable points and uniformly expansive points, respectively. Assume that the set of periodic points and the set of periodic shadowable points of a homeomorphism on a compact metric space are dense in $X$. Then we show that a homeomorphism has the periodic shadowing property if and only if so is the restricted map to the set of periodic shadowable points. We also give some examples related to our results.
TOPOLOGICAL STABILITY IN HYPERSPACE DYNAMICAL SYSTEMS
Koo, Namjip,Lee, Hyunhee,Tsegmid, Nyamdavaa Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.4
In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.
DYNAMICS OF RANDOM DYNAMICAL SYSTEMS
Enkhbayar Azjargal,Zorigt Choinkhor,Nyamdavaa Tsegmid Korean Mathematical Society 2023 대한수학회보 Vol.60 No.4
In this paper, we introduce the concept of ω-expansive of random map on compact metric spaces 𝓟. Also we introduce the definitions of positively, negatively shadowing property and shadowing property for two-sided RDS. Then we show that if 𝜑 is ω-expansive and has the shadowing property for ω, then 𝜑 is topologically stable for ω.
ON PERIODIC SHADOWING OF INDUCED HYPERSPACE MAPS
Namjip Koo,Hyunhee Lee,Nyamdavaa Tsegmid 충청수학회 2021 충청수학회지 Vol.34 No.1
In this paper we deal with the preservation of the pe- riodic shadowing property of induced hyperspatial systems. More precisely, we show that an expansive system has the periodic shad- owing property if and only if its induced hyperspatial system has the periodic shadowing property.