scholarly journals The average-shadowing property and topological ergodicity

2007 ◽  
Vol 206 (2) ◽  
pp. 796-800 ◽  
Author(s):  
Rongbao Gu
Keyword(s):  
Shadowing Property

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

scholarly journals Quasi-shadowing for partially hyperbolic diffeomorphisms

2014 ◽  
Vol 35 (2) ◽  
pp. 412-430 ◽  
Author(s):  
HUYI HU ◽  
YUNHUA ZHOU ◽  
YUJUN ZHU
Keyword(s):  
Spectral Decomposition ◽  
Hyperbolic Systems ◽  
Decomposition Theorem ◽  
Closing Lemma ◽  
Shadowing Property ◽  
Hyperbolic Diffeomorphisms ◽  
Uniformly Hyperbolic Systems ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Partially Hyperbolic Diffeomorphism

AbstractA partially hyperbolic diffeomorphism $f$ has the quasi-shadowing property if for any pseudo orbit $\{x_{k}\}_{k\in \mathbb{Z}}$, there is a sequence of points $\{y_{k}\}_{k\in \mathbb{Z}}$ tracing it in which $y_{k+1}$ is obtained from $f(y_{k})$ by a motion ${\it\tau}$ along the center direction. We show that any partially hyperbolic diffeomorphism has the quasi-shadowing property, and if $f$ has a $C^{1}$ center foliation then we can require ${\it\tau}$ to move the points along the center foliation. As applications, we show that any partially hyperbolic diffeomorphism is topologically quasi-stable under $C^{0}$-perturbation. When $f$ has a uniformly compact $C^{1}$ center foliation, we also give partially hyperbolic diffeomorphism versions of some theorems which hold for uniformly hyperbolic systems, such as the Anosov closing lemma, the cloud lemma and the spectral decomposition theorem.

Inverse shadowing property of transitivity with G-and topological G

2020 ◽  
Author(s):  
Iftichar M. T. AL-Shara’a ◽  
MayAlaa Abdul-khaleq AL-Yaseen
Keyword(s):  
Shadowing Property ◽  
Inverse Shadowing

scholarly journals Vector fields with the oriented shadowing property

2010 ◽  
Vol 248 (6) ◽  
pp. 1345-1375 ◽  
Author(s):  
Sergei Yu. Pilyugin ◽  
Sergey B. Tikhomirov
Keyword(s):  
Vector Fields ◽  
Shadowing Property

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 Some General Properties of the Inverse Shadowing Property

2018 ◽  
Vol 26 (10) ◽  
pp. 176-180 ◽  
Author(s):  
Iftichar Mudhar Talb Al-Shara'a ◽  
Sarah Khadr Khazem Al Sultani
Keyword(s):  
Metric Space ◽  
Shadowing Property ◽  
General Properties ◽  
Inverse Shadowing

The inverse shadowing property is concentrated, it has important properties and applications in maths. In this paper, some general properties of this concept are proved.  Let  ( be   a metric space: ( → (  be maps have the inverse shadowing property. We show the maps    ∘ ,    have the inverse shadowing property. If and :( , ????) →( ,????) are mapped on a metric space ( ,????) have the inverse shadowing property, We show the maps   +   and   .  have the inverse shadowing property.

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