A note on mixing properties of invertible extensions

Ward, Thomas B. and Morris, Gary (1997) A note on mixing properties of invertible extensions. Acta Mathematica Universitatis Comenianae, 66 (2). pp. 307-311.

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The natural invertible extension T* of an Nd-action T has been studied by Lacroix. He showed that T* may fail to be mixing even if T is mixing for d ³ 2. We extend this observation by showing that if T is mixing on (k+1) sets then T* is in general mixing on no more than k sets, simply because Nd has a corner. Several examples are constructed when d = 2: (i) a mixing T for which T*(n,m) has an identity factor whenever n·m < 0; (ii) a mixing T for which T* is rigid but T*(n,m) is mixing for all (n,m) ¹ (0,0); (iii) a T mixing on 3 sets for which T* is not mixing on 3 sets.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 15 Dec 2022 02:04
URI: https://ueaeprints.uea.ac.uk/id/eprint/18609

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