scholarly journals AVERAGE CHAIN TRANSITIVITY AND THE ALMOST AVERAGE SHADOWING PROPERTY

2017 ◽  
Vol 32 (1) ◽  
pp. 201-214 ◽  
Author(s):  
Ruchi Das ◽  
Mukta Garg
Keyword(s):  
Shadowing Property ◽  
Chain Transitivity

Chain transitivity and variations of the shadowing property

2014 ◽  
Vol 35 (7) ◽  
pp. 2044-2052 ◽  
Author(s):  
WILLIAM R. BRIAN ◽  
JONATHAN MEDDAUGH ◽  
BRIAN E. RAINES
Keyword(s):  
Arbitrary Sequence ◽  
Ramsey Property ◽  
Shadowing Property ◽  
Chain Transitivity ◽  
A Chain

We show that, under the assumption of chain transitivity, the shadowing property is equivalent to the thick shadowing property. We also show that, if ${\mathcal{F}}$ is a family with the Ramsey property, then an arbitrary sequence of points in a chain transitive space can be ${\it\varepsilon}$-shadowed (for any ${\it\varepsilon}$) on a set in ${\mathcal{F}}$.

Shadowing and average shadowing properties for iterated function systems

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Alireza Zamani Bahabadi
Keyword(s):  
Iterated Function System ◽  
Iterated Function Systems ◽  
Function System ◽  
Skew Product ◽  
Shadowing Property ◽  
Iterated Function ◽  
Chain Transitivity

AbstractIn this paper, we introduce the definitions of shadowing and average shadowing properties for iterated function systems and give some examples characterizing these definitions. We prove that an iterated function system has the shadowing property if and only if the step skew product corresponding to the iterated function system has the shadowing property. Also, we study some notions such as transitivity, chain transitivity, chain mixing and mixing for iterated function systems.

scholarly journals Variants of shadowing properties for iterated function systems on uniform spaces

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2565-2572
Author(s):  
Radhika Vasisht ◽  
Mohammad Salman ◽  
Ruchi Das
Keyword(s):  
Iterated Function System ◽  
Iterated Function Systems ◽  
Function System ◽  
Uniform Spaces ◽  
Shadowing Property ◽  
Topological Mixing ◽  
Topologically Transitive ◽  
Iterated Function ◽  
Chain Transitivity

In this paper, the notions of topological shadowing, topological ergodic shadowing, topological chain transitivity and topological chain mixing are introduced and studied for an iterated function system (IFS) on uniform spaces. It is proved that if an IFS has topological shadowing property and is topological chain mixing, then it has topological ergodic shadowing and it is topological mixing. Moreover, if an IFS has topological shadowing property and is topological chain transitive, then it is topologically ergodic and hence topologically transitive. Also, these notions are studied for the product IFS on uniform spaces.

scholarly journals G -Chain Mixing and G -Chain Transitivity in Metric G-Space

2022 ◽  
Vol 2022 ◽  
pp. 1-7
Author(s):  
Zhanjiang Ji
Keyword(s):  
Positive Integer ◽  
Shadowing Property ◽  
Open Set ◽  
Chain Transitivity ◽  
Dynamical Properties

Firstly, we introduce the concept of G -chain mixing, G -mixing, and G -chain transitivity in metric G -space. Secondly, we study their dynamical properties and obtain the following results. (1) If the map f has the G -shadowing property, then the map f is G -chain mixed if and only if the map f is G -mixed. (2) The map f is G -chain transitive if and only if for any positive integer k ≥ 2 , the map f k is G -chain transitive. (3) If the map f is G -pointwise chain recurrent, then the map f is G -chain transitive. (4) If there exists a nonempty open set U satisfying G U = U , U ¯ ≠ X , and f U ¯ ⊂ U , then we have that the map f is not G -chain transitive. These conclusions enrich the theory of G -chain mixing, G -mixing, and G -chain transitivity in metric G -space.

Some dynamical properties for free semigroup actions

2018 ◽  
Vol 18 (04) ◽  
pp. 1850032 ◽  
Author(s):  
Huihui Hui ◽  
Dongkui Ma
Keyword(s):  
Metric Space ◽  
Free Semigroup ◽  
Semigroup Action ◽  
Compact Metric Space ◽  
Shadowing Property ◽  
Semigroup Actions ◽  
Specification Property ◽  
Chain Transitivity ◽  
Weakly Mixing ◽  
Dynamical Properties

In this paper, we introduce the notions of weakly mixing and totally transitivity for a free semigroup action. Let [Formula: see text] be a free semigroup acting on a compact metric space generated by continuous open self-maps. Assuming shadowing for [Formula: see text] we relate the average shadowing property of [Formula: see text] to totally transitivity and its variants. Also, we study some properties such as mixing, shadowing and average shadowing properties, transitivity, chain transitivity, chain mixing and specification property for a free semigroup action.

Shadowing, ergodic shadowing and uniform spaces

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5117-5124 ◽  
Author(s):  
Seyyed Ahmadi
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Metric Spaces ◽  
Uniform Spaces ◽  
Shadowing Property ◽  
Chain Transitivity ◽  
Metrizable Spaces

We introduce and study the topological concepts of ergodic shadowing, chain transitivity and topological ergodicity for dynamical systems on non-compact non-metrizable spaces. These notions generalize the relevant concepts for metric spaces. We prove that a dynamical system with topological ergodic shadowing property is topologically chain transitive, and that topological chain transitivity together with topological shadowing property implies topological ergodicity.

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.

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