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Homeomorphisms with the whole compacta being scrambled sets

Published online by Cambridge University Press:  26 March 2001

WEN HUANG  and
XIANGDONG YE
WEN HUANG
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China (e-mail: yexd@ustc.edu.cn)
XIANGDONG YE
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China (e-mail: yexd@ustc.edu.cn)
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Abstract

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A homeomorphism on a metric space (X,d) is completely scrambled if for each x\not= y\in X, \lim sup_{n\longrightarrow +\infty} d(f^n(x),f^n(y))>0 and \lim inf_{n\ longrightarrow +\infty}d(f^n(x),f^n(y))=0. We study the basic properties of completely scrambled homeomorphisms on compacta and show that there are ‘many’ compacta admitting completely scrambled homeomorphisms, which include some countable compacta (we give a characterization), the Cantor set and continua of arbitrary dimension.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 1 , February 2001 , pp. 77 - 91
Copyright
© 2001 Cambridge University Press