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Periodic point data detects subdynamics in entropy rank one
, 2006
"... A framework for understanding the geometry of continuous actions of Z d was developed by Boyle and Lind using the notion of expansive behavior along lowerdimensional subspaces. For algebraic Z dactions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponen ..."
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Cited by 6 (5 self)
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A framework for understanding the geometry of continuous actions of Z d was developed by Boyle and Lind using the notion of expansive behavior along lowerdimensional subspaces. For algebraic Z dactions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the expansive subdynamics. Moreover, the finer structure of the nonexpansive set is visible in the topological and smooth structure of a set of functions associated to the periodic point data.
ISOMORPHISM RIGIDITY IN ENTROPY RANK TWO
, 2003
"... Abstract. We study the rigidity properties of a class of algebraic Z 3actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine subset. This is applied to show isomorphism rigidity for such actions, and to provide exampl ..."
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Cited by 1 (0 self)
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Abstract. We study the rigidity properties of a class of algebraic Z 3actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine subset. This is applied to show isomorphism rigidity for such actions, and to provide examples of nonisomorphic Z 3actions with all their Z 2subactions isomorphic. The proofs use lexicographic halfspace entropies and total ergodicity along critical directions. 1.