Linear transitivity on compact connected hyperspace dynamics

Yuhu Wu; Xiaoping Xue; Donghai Ji

Linear transitivity on compact connected hyperspace dynamics

Yuhu Wu^*
, Xiaoping Xue
, Donghai Ji

^*Corresponding author for this work

School of Mathematics

Harbin University of Science and Technology

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let f be a linear operator on a Banach space X. In this paper we prove that the transitivity of induced compact connected hyperspace dynamical system (K K(X),f̄_KK) is equivalent to weak mixing of the base dynamical system (X, f). Furthermore, we deduce that if X is separable, then (X, f) satisfies the hypercyclicity criterion if and only if (K K(X), f̄_KK) is transitive.

Original language	English
Pages (from-to)	523-534
Number of pages	12
Journal	Dynamic Systems and Applications
Volume	21
Issue number	4
State	Published - Dec 2012

Keywords

Compact connected hyperspace
Hypercyclicity criterion
Induced hyperspace dynamical system
Topological transitivity
Weak mixing

Cite this

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title = "Linear transitivity on compact connected hyperspace dynamics",

abstract = "Let f be a linear operator on a Banach space X. In this paper we prove that the transitivity of induced compact connected hyperspace dynamical system (K K(X),{\=f}KK) is equivalent to weak mixing of the base dynamical system (X, f). Furthermore, we deduce that if X is separable, then (X, f) satisfies the hypercyclicity criterion if and only if (K K(X), {\=f}KK) is transitive.",

keywords = "Compact connected hyperspace, Hypercyclicity criterion, Induced hyperspace dynamical system, Topological transitivity, Weak mixing",

author = "Yuhu Wu and Xiaoping Xue and Donghai Ji",

year = "2012",

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journal = "Dynamic Systems and Applications",

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T1 - Linear transitivity on compact connected hyperspace dynamics

AU - Wu, Yuhu

AU - Xue, Xiaoping

AU - Ji, Donghai

PY - 2012/12

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N2 - Let f be a linear operator on a Banach space X. In this paper we prove that the transitivity of induced compact connected hyperspace dynamical system (K K(X),f̄KK) is equivalent to weak mixing of the base dynamical system (X, f). Furthermore, we deduce that if X is separable, then (X, f) satisfies the hypercyclicity criterion if and only if (K K(X), f̄KK) is transitive.

AB - Let f be a linear operator on a Banach space X. In this paper we prove that the transitivity of induced compact connected hyperspace dynamical system (K K(X),f̄KK) is equivalent to weak mixing of the base dynamical system (X, f). Furthermore, we deduce that if X is separable, then (X, f) satisfies the hypercyclicity criterion if and only if (K K(X), f̄KK) is transitive.

KW - Compact connected hyperspace

KW - Hypercyclicity criterion

KW - Induced hyperspace dynamical system

KW - Topological transitivity

KW - Weak mixing

UR - https://www.scopus.com/pages/publications/84871867689

M3 - 文章

AN - SCOPUS:84871867689

SN - 1056-2176

VL - 21

SP - 523

EP - 534

JO - Dynamic Systems and Applications

JF - Dynamic Systems and Applications

IS - 4

ER -

Linear transitivity on compact connected hyperspace dynamics

Abstract

Keywords

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