15 February 2003 Zero-entropy algebraic $\mathbb {Z}\sp d$-actions that do not exhibit rigidity
Siddhartha Bhattacharya
Duke Math. J. 116(3): 471-476 (15 February 2003). DOI: 10.1215/S0012-7094-03-11633-6

Abstract

We show that there exist mixing zero-entropy algebraic $\mathbb {Z}\sp 8$-actions that are measurably and topologically conjugate but not algebraically conjugate. This result gives the first known examples of mixing zero-entropy algebraic $\mathbb {Z}\sp d$-actions that do not have rigidity properties, and it provides a negative answer to the isomorphism rigidity problem raised in B. Kitchens and K. Schmidt (Isomorphism rigidity of irreducible algebraic $\mathbb {Z}\sp d$-actions, Invent. Math. 142 (2000), 559‒577) and Schmidt ("The dynamics of algebraic $\mathbb {Z}\sp d$-actions" in European Congress of Mathematics (Barcelona, 2000), Vol. 1, Progr. Math. 201, Birkhäuser, Basel, 2001, 543‒553).

Citation

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Siddhartha Bhattacharya. "Zero-entropy algebraic $\mathbb {Z}\sp d$-actions that do not exhibit rigidity." Duke Math. J. 116 (3) 471 - 476, 15 February 2003. https://doi.org/10.1215/S0012-7094-03-11633-6

Information

Published: 15 February 2003
First available in Project Euclid: 26 May 2004

zbMATH: 1018.37004
MathSciNet: MR1958095
Digital Object Identifier: 10.1215/S0012-7094-03-11633-6

Subjects:
Primary: 37A15
Secondary: 22D40 , 28D15 , 37A35

Rights: Copyright © 2003 Duke University Press

Vol.116 • No. 3 • 15 February 2003
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