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.