More on induced maps on n-fold symmetric product suspensions

Barragán, Franco; Macı́as, Sergio; Tenorio, Jesús F.

doi:10.3336/gm.50.2.15

Cited by 9 publications

(7 citation statements)

References 9 publications

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“…On the other hand, by theorem 3.11, we have that (5) and 7are equivalent. It follows from diagram 3 that (6) implies (7). Now, if (F n (X), F n (f )) is weakly mixing, then by [8,Theorem 3.4], (SF n m (X), SF n m (f )) is weakly mixing.…”

Section: Dynamic Properties Of the Dynamical Systemmentioning

confidence: 98%

“…If n is a positive integer, the induced map to the hyperspace C n (X) is the restriction of 2 f to C n (X), and is denoted by C n (f ) and the induced map to the hyperspace F n (X) is simply the restriction of 2 f to F n (X) which is denoted by F n (f ). This last map, F n (f ), induces a map on the space SF n (X) which is denoted by SF n (f ) : SF n (X) → SF n (X) [5,7]. Thus, the dynamical system (X, f ) induces the dynamical systems (2 X , 2 f ), (C n (X), C n (f )), (F n (X), F n (f )) and (SF n (X), SF n (f )).…”

Section: Introductionmentioning

confidence: 99%

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Dynamic properties of the dynamical system SFnm(X), SFnm(f))

2020

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Let X be a continuum and let n be a positive integer. We consider the hyperspaces Fn(X) and SFn(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SFnm(X). For a given map f : X → X, we consider the induced maps Fn(f) : Fn(X) → Fn(X), SFn(f) : SFn(X) → SFn(X) and SFnm(f) : SFnm(X) → SFnm(X). In this paper, we introduce the dynamical system (SFnm(X), SFnm (f)) and we investigate some relationships between the dynamical systems (X, f), (Fn(X), Fn(f)), (SFn(X), SFn(f)) and (SFnm(X), SFnm(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.

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Section: Dynamic Properties Of the Dynamical Systemmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Dynamic properties of the dynamical system SFnm(X), SFnm(f))

2020

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“…Readers especially interested in this topic are referred, for example, to [5], [7], [8], [11], [12], [16], [17]. Regarding induced mappings in quotient hyperspaces we refer the reader, for example, to [1], [3], [4], [6], [10], [30].…”

Section: Introductionmentioning

confidence: 99%

Induced mappings on $C_n(X)/{C_n}_K(X)$

2021

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Given a continuum $X$ and $n\in\mathbb{N}$. Let $C_n(X)$ be the hyperspace of all nonempty closed subsets of $X$ with at most $n$ components. Let ${C_n}_K(X)$ be the hyperspace of all elements in $C_n(X)$ containing $K$ where $K$ is a compact subset of $X$. $C^n_K(X)$ denotes the quotient space $C_n(X)/{C_n}_K(X)$. Given a mapping $f:X\to Y$ between continua, let $C_n(f):C_n(X)\to C_n(Y)$ be the induced mapping by $f$, defined by $C_n(f)(A)=f(A)$. We denote the natural induced mapping between $C^n_K(X)$ and $C^n_{f(K)}(Y)$ by $C^n_K(f)$. In this paper, we study relationships among the mappings $f$, $C_n(f)$ and $C^n_K(f)$ for the following classes of mappings: almost monotone, atriodic, confluent, joining, light, monotone, open, OM, pseudo-confluent, quasi-monotone, semi-confluent, strongly freely decomposable, weakly confluent, and weakly monotone.

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“…126], SF n (f ) is continuous, it is called induced map of f on n-fold symmetric product suspension (see [4] and [6]). In addition, the diagram:…”

Section: Exactmentioning

confidence: 99%

“…The induced map to the other hyperspaces mentioned are simply the restriction of 2 f to each of such hyperspaces, denoted by C n (f ) and F n (f ), respectively, for each positive integer n. If n is an integer greater than or equal to two, we consider the induced map SF n (f ) : SF n (X) → SF n (X), which is called induced map of f on the n-fold symmetric product suspension of X. Some topological properties of SF n (f ) are studied in [4] and [6].…”

Section: Introductionmentioning

confidence: 99%

Dynamic properties for the induced maps on n-fold symmetric product suspensions

Barragán

Santiago-Santos

Tenorio

2016

Glas. Mat. Ser. III

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Abstract. Let X be a continuum. For any positive integer n we consider the hyperspace Fn(X) and if n is greater than or equal to two, we consider the quotient space SF n(X ) defined in [3]. For a given map f : X → X, we consider the induced maps Fn(f ) : Fn(X) → Fn(X) and SFn(f ) : SF n(X ) → SF n(X ) defined in [4]. Let M be one of the following classes of maps: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, minimal, irreducible, feebly open and turbulent. In this paper we study the relationships between the following statements: f ∈ M, Fn(f ) ∈ M and SF n(f ) ∈ M.

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More on induced maps on n-fold symmetric product suspensions

Cited by 9 publications

References 9 publications

Dynamic properties of the dynamical system SFnm(X), SFnm(f))

Dynamic properties of the dynamical system SFnm(X), SFnm(f))

Induced mappings on $C_n(X)/{C_n}_K(X)$

Dynamic properties for the induced maps on n-fold symmetric product suspensions

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