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

详细信息    查看全文

• 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 class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si4.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=69ba3b6c5a33b28845d6ae1a10ca9c54">class="imgLazyJSB inlineImage" height="21" width="95" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0362546X14001175-si4.gif">class="mathContainer hidden">class="mathCode">$(\underset{鉄?/mo>}{lim}(X,f),{蟽}_f)$ of a dynamical system class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si5.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=589041f89d255538011738e3e8e0d29e" title="Click to view the MathML source">(X,f)class="mathContainer hidden">class="mathCode">$(X,f)$ is class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si6.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=9c9ab4519e89b1bcd18b2d296ff13e26" title="Click to view the MathML source">鈩?/span>class="mathContainer hidden">class="mathCode">$\mathrm{鈩?/mi>}$-transitive (resp., class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si7.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=ee67afd11b2e190ef684cdf5116d7b1f" title="Click to view the MathML source">鈩?/span>class="mathContainer hidden">class="mathCode">$\mathrm{鈩?/mi>}$-mixing, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si8.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=c4892f457f2ec79ba6b7df343d81a1b6" title="Click to view the MathML source">(鈩?sub>1,鈩?sub>2)class="mathContainer hidden">class="mathCode">$({\mathrm{鈩?/mi>}}_1,{\mathrm{鈩?/mi>}}_2)$-everywhere chaotic) if and only if the system class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si9.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=9c3fe64d9b45b9a526673739ae107513">class="imgLazyJSB inlineImage" height="20" width="155" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0362546X14001175-si9.gif">class="mathContainer hidden">class="mathCode">$({\cap }_{n=0}^{\infty }{f}^n\left(X\right),f{|}_{{\cap }_{n=0}^{\infty }{f}^n\left(X\right)})$ is class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si10.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=e2114058f8269ee156ed650c279f3d07" title="Click to view the MathML source">鈩?/span>class="mathContainer hidden">class="mathCode">$\mathrm{鈩?/mi>}$-transitive (resp., class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si11.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=25095067e7c41d1a33d42ab9116014e4" title="Click to view the MathML source">鈩?/span>class="mathContainer hidden">class="mathCode">$\mathrm{鈩?/mi>}$-mixing, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si12.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=fac75d9125c997692156f2c0c382bdc8" title="Click to view the MathML source">(鈩?sub>1,鈩?sub>2)class="mathContainer hidden">class="mathCode">$({\mathrm{鈩?/mi>}}_1,{\mathrm{鈩?/mi>}}_2)$-everywhere chaotic), where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si13.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=54158f7d31460bf7c4a5c3f8d45bdcaa" title="Click to view the MathML source">鈩?/span>class="mathContainer hidden">class="mathCode">$\mathrm{鈩?/mi>}$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si14.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=d74d168396d35b7ad1a9f16f8046c9a7" title="Click to view the MathML source">鈩?sub>1class="mathContainer hidden">class="mathCode">${\mathrm{鈩?/mi>}}_1$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X14001175&_mathId=si15.gif&_user=111111111&_pii=S0362546X14001175&_rdoc=1&_issn=0362546X&md5=ec4705a2c2b65e4e5389d0b8a4ffb2f4" title="Click to view the MathML source">鈩?sub>2class="mathContainer hidden">class="mathCode">${\mathrm{鈩?/mi>}}_2$ are Furstenberg families.