A note on mixing properties of invertible extensions

Thomas B. Ward, Gary Morris

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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.
Original languageEnglish
Pages (from-to)307-311
Number of pages5
JournalActa Mathematica Universitatis Comenianae
Issue number2
Publication statusPublished - 1997

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