F-mixing property and (F1, F2)-everywhere chaos of inverse limit dynamical systems

Xinxing Wu; Xiong Wang; Guanrong Chen

doi:10.1016/j.na.2014.03.023

F-mixing property and (F₁, F₂)-everywhere chaos of inverse limit dynamical systems

Xinxing Wu, Xiong Wang^*, Guanrong Chen

^*Corresponding author for this work

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

6 Citations (Scopus)

Abstract

This paper investigates some chaotic properties via Furstenberg families generated by inverse limit dynamical systems. It is proved that the inverse limit dynamical system (lim_←(X, ƒ), σ_ƒ) of a dynamical system (X, ƒ) is F-transitive (resp., F-mixing, (F₁, F₂)-everywhere chaotic) if and only if the system (∩^∞n₌₀ ƒⁿ (X), ƒ|∩^∞_n=0 ^ƒn (X)) is F-transitive (resp., F-mixing, (F₁, F₂)-everywhere chaotic), where F, F₁ and F₂ are Furstenberg families.

Original language	English
Pages (from-to)	147-155
Journal	Nonlinear Analysis: Theory, Methods & Applications
Volume	104
Online published	16 Apr 2014
DOIs	https://doi.org/10.1016/j.na.2014.03.023
Publication status	Published - Jul 2014

Research Keywords

Inverse limit system
F-mixing
F-transitivity
(F1, F2)-everywhere chaos

Access Output

10.1016/j.na.2014.03.023

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{303bef70b5fb4f19ad423f51e6f35ac6,

title = "F-mixing property and (F1, F2)-everywhere chaos of inverse limit dynamical systems",

abstract = "This paper investigates some chaotic properties via Furstenberg families generated by inverse limit dynamical systems. It is proved that the inverse limit dynamical system (lim←(X, ƒ), σƒ) of a dynamical system (X, ƒ) is F-transitive (resp., F-mixing, (F1, F2)-everywhere chaotic) if and only if the system (∩∞n=0 ƒn (X), ƒ|∩∞n=0 ƒn (X)) is F-transitive (resp., F-mixing, (F1, F2)-everywhere chaotic), where F, F1 and F2 are Furstenberg families.",

keywords = "Inverse limit system, F-mixing, F-transitivity, (F1, F2)-everywhere chaos",

author = "Xinxing Wu and Xiong Wang and Guanrong Chen",

year = "2014",

month = jul,

doi = "10.1016/j.na.2014.03.023",

language = "English",

volume = "104",

pages = "147--155",

journal = "Nonlinear Analysis: Theory, Methods & Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - F-mixing property and (F1, F2)-everywhere chaos of inverse limit dynamical systems

AU - Wu, Xinxing

AU - Wang, Xiong

AU - Chen, Guanrong

PY - 2014/7

Y1 - 2014/7

N2 - This paper investigates some chaotic properties via Furstenberg families generated by inverse limit dynamical systems. It is proved that the inverse limit dynamical system (lim←(X, ƒ), σƒ) of a dynamical system (X, ƒ) is F-transitive (resp., F-mixing, (F1, F2)-everywhere chaotic) if and only if the system (∩∞n=0 ƒn (X), ƒ|∩∞n=0 ƒn (X)) is F-transitive (resp., F-mixing, (F1, F2)-everywhere chaotic), where F, F1 and F2 are Furstenberg families.

AB - This paper investigates some chaotic properties via Furstenberg families generated by inverse limit dynamical systems. It is proved that the inverse limit dynamical system (lim←(X, ƒ), σƒ) of a dynamical system (X, ƒ) is F-transitive (resp., F-mixing, (F1, F2)-everywhere chaotic) if and only if the system (∩∞n=0 ƒn (X), ƒ|∩∞n=0 ƒn (X)) is F-transitive (resp., F-mixing, (F1, F2)-everywhere chaotic), where F, F1 and F2 are Furstenberg families.

KW - Inverse limit system

KW - F-mixing

KW - F-transitivity

KW - (F1, F2)-everywhere chaos

UR - http://www.scopus.com/inward/record.url?scp=84898626598&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84898626598&origin=recordpage

U2 - 10.1016/j.na.2014.03.023

DO - 10.1016/j.na.2014.03.023

M3 - RGC 21 - Publication in refereed journal

SN - 0362-546X

VL - 104

SP - 147

EP - 155

JO - Nonlinear Analysis: Theory, Methods & Applications

JF - Nonlinear Analysis: Theory, Methods & Applications

ER -