-mixing property and -everywhere chaos of inverse limit dynamical systems

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• 作者：Xinxing Wu^a ; ^b ; ^{wuxinxing5201314@163.com" class="auth_mail} ; Xiong Wang^b ; ^{wangxiong8686@gmail.com" class="auth_mail} ; Guanrong Chen^b ; ^{gchen@ee.cityu.edu.hk" class="auth_mail}
• 关键词：primary ; 54H20 ; 37B99 ; secondary ; 54H20 ; 37D45 ; 37B10 ; 37B20 ; 37B40 ; 34C28
• 刊名：Nonlinear Analysis
• 出版年：July 2014
• 年：2014
• 卷：104
• 期：Complete
• 页码：147-155
• 全文大小：428 K

文摘

This paper investigates some chaotic properties via Furstenberg families generated by inverse limit dynamical systems. It is proved that the inverse limit dynamical system $(\underset{鉄?/mo>}{lim}(X,f),{蟽}_f)$ of a dynamical system (X,f)$(X,f)$ is 鈩?/span>$\mathrm{鈩?/mi>}$-transitive (resp., 鈩?/span>$\mathrm{鈩?/mi>}$-mixing, (鈩?sub>1,鈩?sub>2)$({\mathrm{鈩?/mi>}}_1,{\mathrm{鈩?/mi>}}_2)$-everywhere chaotic) if and only if the system $({\cap }_{n=0}^{\infty }{f}^n\left(X\right),f{|}_{{\cap }_{n=0}^{\infty }{f}^n\left(X\right)})$ is 鈩?/span>$\mathrm{鈩?/mi>}$-transitive (resp., 鈩?/span>$\mathrm{鈩?/mi>}$-mixing, (鈩?sub>1,鈩?sub>2)$({\mathrm{鈩?/mi>}}_1,{\mathrm{鈩?/mi>}}_2)$-everywhere chaotic), where 鈩?/span>$\mathrm{鈩?/mi>}$, 鈩?sub>1${\mathrm{鈩?/mi>}}_1$ and 鈩?sub>2${\mathrm{鈩?/mi>}}_2$ are Furstenberg families.