Zero-entropy algebraic $\mathbb {Z}\sp d$-actions that do not exhibit rigidity
Bhattacharya, Siddhartha
Duke Math. J., Tome 120 (2003) no. 3, p. 471-476 / Harvested from Project Euclid
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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).
Publié le : 2003-03-15
Classification:  37A15,  22D40,  28D15,  37A35 
@article{1085598299,
     author = {Bhattacharya, Siddhartha},
     title = {Zero-entropy algebraic $\mathbb {Z}\sp d$-actions that do not exhibit rigidity},
     journal = {Duke Math. J.},
     volume = {120},
     number = {3},
     year = {2003},
     pages = { 471-476},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1085598299}
}

Bhattacharya, Siddhartha. Zero-entropy algebraic $\mathbb {Z}\sp d$-actions that do not exhibit rigidity. Duke Math. J., Tome 120 (2003) no. 3, pp.  471-476. http://gdmltest.u-ga.fr/item/1085598299/