Chain transitivity in hyperspaces

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• 作者：Leobardo Ferná ; ndez ; ^a ; ^{l.fernandez@bham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; ^{leobardof@ciencias.unam.mx" class="auth_mail" title="E-mail the corresponding author} ; ^{leobardof@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Chris Good^a ; ^{c.good@bham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Mate Puljiz^a ; ^{MXP243@student.bham.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Á ; rtico Ramí ; rez^b ; ^{artico@ciencias.unam.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：δ-pseudo orbit ; Induced map ; Chain transitivity ; Chain weakly mixing ; Exact by chains
• 刊名：Chaos, Solitons & Fractals
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：81
• 期：part_PA
• 页码：83-90
• 全文大小：501 K

文摘

Given a non-empty compact metric space X and a continuous function f: X → X, we study the dynamics of the induced maps on the hyperspace of non-empty compact subsets of X and on various other invariant subspaces thereof, in particular symmetric products. We show how some important dynamical properties transfer across induced systems. These amongst others include, chain transitivity, chain (weakly) mixing, chain recurrence, exactness by chains. From our main theorem we derive an ε-chain version of Furstenberg’s celebrated 2 implies n Theorem. We also show the implications our results have for dynamics on continua.