scholarly journals Shadowing property for inverse limit spaces

1992 ◽  
Vol 115 (2) ◽  
pp. 573-573 ◽  
Author(s):  
Liang Chen ◽  
Shi Hai Li
Keyword(s):  
Inverse Limit ◽  
Shadowing Property ◽  
Inverse Limit Spaces

scholarly journals Inverse Limit Spaces with Various Shadowing Property

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Ali Barzanouni
Keyword(s):  
Inverse Limit ◽  
Shadowing Property ◽  
Inverse Limit Spaces ◽  
Limit Space ◽  
Inverse Shadowing ◽  
Shift Map ◽  
Inverse Limit Space ◽  
The Relationship

We discuss the relationship between ergodic shadowing property and inverse shadowing property offand that of the shift map σfon the inverse limit space.

scholarly journals The G-sequence shadowing property and G-equicontinuity of the inverse limit spaces under group action

2021 ◽  
Vol 19 (1) ◽  
pp. 1290-1298
Author(s):  
Zhanjiang Ji
Keyword(s):  
Group Action ◽  
Inverse Limit ◽  
The Self ◽  
Recurrent Point ◽  
Shadowing Property ◽  
Inverse Limit Spaces ◽  
Limit Space ◽  
Dynamical Properties ◽  
Inverse Limit Space

Abstract First, we give the concepts of G-sequence shadowing property, G-equicontinuity and G-regularly recurrent point. Second, we study their dynamical properties in the inverse limit space under group action. The following results are obtained. (1) The self-mapping f f has the G-sequence shadowing property if and only if the shift mapping σ \sigma has the G ¯ \overline{G} -sequence shadowing property; (2) The self-mapping f f is G-equicontinuous if and only if the shift mapping σ \sigma is G ¯ \overline{G} -equicontinuous; (3) R R G ¯ ( σ ) = lim ← ( R R G ( f ) , f ) R{R}_{\overline{G}}\left(\sigma )=\underleftarrow{\mathrm{lim}}\left(R{R}_{G}(f),f) . These conclusions make up for the lack of theory in the inverse limit space under group action.

On shadowing property for inverse limit spaces

2008 ◽  
Vol 58 (1) ◽  
Author(s):  
Ekta Shah ◽  
T. Das
Keyword(s):  
Inverse Limit ◽  
Shadowing Property ◽  
Inverse Limit Spaces ◽  
Limit Space ◽  
Shift Map ◽  
Inverse Limit Space

AbstractWe study here the G-shadowing property of the shift map σ on the inverse limit space X f, generated by an equivariant self-map f on a metric G-space X.

Invariants of weak equivalence in primitive matrices

2000 ◽  
Vol 20 (2) ◽  
pp. 611-626 ◽  
Author(s):  
RICHARD SWANSON ◽  
HANS VOLKMER
Keyword(s):  
Inverse Limit ◽  
Direct Application ◽  
Topological Classification ◽  
Weak Equivalence ◽  
Transition Matrices ◽  
Inverse Limit Spaces ◽  
Positive Dimension ◽  
One Dimensional ◽  
Dimension Group

Weak equivalence of primitive matrices is a known invariant arising naturally from the study of inverse limit spaces. Several new invariants for weak equivalence are described. It is proved that a positive dimension group isomorphism is a complete invariant for weak equivalence. For the transition matrices corresponding to periodic kneading sequences, the discriminant is proved to be an invariant when the characteristic polynomial is irreducible. The results have direct application to the topological classification of one-dimensional inverse limit spaces.

scholarly journals The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space

2022 ◽  
Vol 2022 ◽  
pp. 1-6
Author(s):  
Zhan jiang Ji
Keyword(s):  
Inverse Limit ◽  
Point Sets ◽  
Recurrent Point ◽  
Shadowing Property ◽  
Limit Space ◽  
Shift Map ◽  
Dynamical Properties ◽  
Definition Of ◽  
Inverse Limit Space

According to the definition of sequence shadowing property and regularly recurrent point in the inverse limit space, we introduce the concept of sequence shadowing property and regularly recurrent point in the double inverse limit space and study their dynamical properties. The following results are obtained: (1) Regularly recurrent point sets of the double shift map σ f ∘ σ g are equal to the double inverse limit space of the double self-map f ∘ g in the regularly recurrent point sets. (2) The double self-map f ∘ g has sequence shadowing property if and only if the double shift map σ f ∘ σ g has sequence shadowing property. Thus, the conclusions of sequence shadowing property and regularly recurrent point are generalized to the double inverse limit space.

scholarly journals On isotopy and unimodal inverse limit spaces

2012 ◽  
Vol 32 (4) ◽  
pp. 1245-1253 ◽  
Author(s):  
Henk Bruin ◽  
◽  
Sonja Štimac ◽  
Keyword(s):  
Inverse Limit ◽  
Inverse Limit Spaces

scholarly journals Inverse Limit Spaces Satisfying a Poincaré Inequality

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Jeff Cheeger ◽  
Bruce Kleiner
Keyword(s):  
Banach Space ◽  
Large Class ◽  
Inverse Limit ◽  
Poincaré Inequality ◽  
Doubling Condition ◽  
Poincare Inequality ◽  
Inverse Limit Spaces ◽  
Inverse Systems ◽  
Nikodym Property

Abstract We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces, and a large class of new examples. As follows easily from [4], generically our examples have the property that they do not bilipschitz embed in any Banach space with Radon-Nikodym property. For Laakso spaces, thiswas noted in [4]. However according to [7] these spaces admit a bilipschitz embedding in L1. For Laakso spaces, this was announced in [5].

scholarly journals G-Expansibility and G-Almost Periodic Point under Topological Group Action

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Zhanjiang Ji
Keyword(s):  
Topological Group ◽  
Periodic Point ◽  
Inverse Limit ◽  
The Self ◽  
Almost Periodic ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Shift Map ◽  
Inverse Limit Space ◽  
Almost Periodic Point

Firstly, the new concepts of G − expansibility, G − almost periodic point, and G − limit shadowing property were introduced according to the concepts of expansibility, almost periodic point, and limit shadowing property in this paper. Secondly, we studied their dynamical relationship between the self-map f and the shift map σ in the inverse limit space under topological group action. The following new results are obtained. Let X , d be a metric G − space and X f , G ¯ ,   d ¯ , σ be the inverse limit space of X , G , d , f . (1) If the map f : X ⟶ X is an equivalent map, then we have A P G ¯ σ = Lim ← A p G f , f . (2) If the map f : X ⟶ X is an equivalent surjection, then the self-map f is G − expansive if and only if the shift map σ is G ¯ − expansive. (3) If the map f : X ⟶ X is an equivalent surjection, then the self-map f has G − limit shadowing property if and only if the shift map σ has G ¯ − limit shadowing property. The conclusions of this paper generalize the corresponding results given in the study by Li, Niu, and Liang and Li . Most importantly, it provided the theoretical basis and scientific foundation for the application of tracking property in computational mathematics and biological mathematics.

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