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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Duke Mathematical Journal
( Vol. 116 NO.3 / (2003))
Zero-Entropy Algebraic $\Bbb{Z}^d$-Actions that Do Not Exhibit Rigidity
Siddhartha Bhattacharya,
Pages. 471-476
Abstract We show that there exist mixing zero-entropy algebraic $Bbb{Z}^8$-actions that are measurably
and topologically conjugate but not algebraically conjugate. This result gives
the first known examples of mixing zero-entropy algebraic $Bbb{Z}^d$-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 $Bbb{Z}^d$-actions, Invent. Math. 142(2000), 559-577) and Schmidt("The dynamics
of algebraic $Bbb{Z}^d$-actions" in European Congress of Mathematics(Barcelona,
2000), Vol. 1, Progr. Math. 201, Birkhauser, Besel, 2001, 543-553).
Contents 1. Introduction
2. Nonrigid actions
Key words
Mathmatical Subject Classification 37A35, 22D40, 28D15