Homeomorphisms with the whole compacta being scrambled sets

Authors
Citation
W. Huang et Xd. Ye, Homeomorphisms with the whole compacta being scrambled sets, ERGOD TH DY, 21, 2001, pp. 77-91
Citations number
20
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
ERGODIC THEORY AND DYNAMICAL SYSTEMS
ISSN journal
0143-3857 → ACNP
Volume
21
Year of publication
2001
Part
1
Pages
77 - 91
Database
ISI
SICI code
0143-3857(200102)21:<77:HWTWCB>2.0.ZU;2-C
Abstract
A homeomorphism on a metric space (X, d) is completely scrambled if for eac h x not equal y is an element of X, lim sup(n--> + infinity) d (f(n)(x), f( n)(y)) > 0 and lim inf(n-->+infinity) d(f(n)(x), f(n)(y)) 0. We study the b asic properties of completely scrambled homeomorphisms on compacta and show that there are 'many' compacta admitting completely scrambled homeomorphis ms, which include some countable compacta (we give a characterization), the Canter set and continua of arbitrary dimension.